수학동아 - 폴리매스

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property CI_URI::$config is deprecated

Filename: core/URI.php

Line Number: 101

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property CI_Router::$uri is deprecated

Filename: core/Router.php

Line Number: 127

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property Contents::$benchmark is deprecated

Filename: core/Controller.php

Line Number: 75

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 14
Function: __construct

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property Contents::$hooks is deprecated

Filename: core/Controller.php

Line Number: 75

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 14
Function: __construct

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property Contents::$config is deprecated

Filename: core/Controller.php

Line Number: 75

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 14
Function: __construct

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property Contents::$log is deprecated

Filename: core/Controller.php

Line Number: 75

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 14
Function: __construct

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property Contents::$utf8 is deprecated

Filename: core/Controller.php

Line Number: 75

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 14
Function: __construct

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property Contents::$uri is deprecated

Filename: core/Controller.php

Line Number: 75

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 14
Function: __construct

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property Contents::$exceptions is deprecated

Filename: core/Controller.php

Line Number: 75

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 14
Function: __construct

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property Contents::$router is deprecated

Filename: core/Controller.php

Line Number: 75

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 14
Function: __construct

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property Contents::$output is deprecated

Filename: core/Controller.php

Line Number: 75

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 14
Function: __construct

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property Contents::$security is deprecated

Filename: core/Controller.php

Line Number: 75

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 14
Function: __construct

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property Contents::$input is deprecated

Filename: core/Controller.php

Line Number: 75

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 14
Function: __construct

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property Contents::$lang is deprecated

Filename: core/Controller.php

Line Number: 75

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 14
Function: __construct

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property Contents::$load is deprecated

Filename: core/Controller.php

Line Number: 78

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 14
Function: __construct

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property CI_Cache::$apc is deprecated

Filename: libraries/Driver.php

Line Number: 188

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Cacher.php
Line: 22
Function: driver

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Cacher.php
Line: 17
Function: initiateCache

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 14
Function: __construct

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property CI_Cache::$file is deprecated

Filename: libraries/Driver.php

Line Number: 188

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Cacher.php
Line: 22
Function: driver

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Cacher.php
Line: 17
Function: initiateCache

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 14
Function: __construct

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property Contents::$cache is deprecated

Filename: core/Loader.php

Line Number: 1279

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Cacher.php
Line: 22
Function: driver

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Cacher.php
Line: 17
Function: initiateCache

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 14
Function: __construct

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property Contents::$cacher is deprecated

Filename: core/Loader.php

Line Number: 1279

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 14
Function: __construct

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property Contents::$jscript is deprecated

Filename: core/Loader.php

Line Number: 1279

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 14
Function: __construct

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Return type of CI_Session_files_driver::open($save_path, $name) should either be compatible with SessionHandlerInterface::open(string $path, string $name): bool, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice

Filename: drivers/Session_files_driver.php

Line Number: 132

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 14
Function: __construct

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Return type of CI_Session_files_driver::close() should either be compatible with SessionHandlerInterface::close(): bool, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice

Filename: drivers/Session_files_driver.php

Line Number: 290

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 14
Function: __construct

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Return type of CI_Session_files_driver::read($session_id) should either be compatible with SessionHandlerInterface::read(string $id): string|false, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice

Filename: drivers/Session_files_driver.php

Line Number: 164

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 14
Function: __construct

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Return type of CI_Session_files_driver::write($session_id, $session_data) should either be compatible with SessionHandlerInterface::write(string $id, string $data): bool, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice

Filename: drivers/Session_files_driver.php

Line Number: 233

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 14
Function: __construct

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Return type of CI_Session_files_driver::destroy($session_id) should either be compatible with SessionHandlerInterface::destroy(string $id): bool, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice

Filename: drivers/Session_files_driver.php

Line Number: 313

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 14
Function: __construct

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Return type of CI_Session_files_driver::gc($maxlifetime) should either be compatible with SessionHandlerInterface::gc(int $max_lifetime): int|false, or the #[\ReturnTypeWillChange] attribute should be used to temporarily suppress the notice

Filename: drivers/Session_files_driver.php

Line Number: 354

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 14
Function: __construct

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: ini_set(): Session ini settings cannot be changed after headers have already been sent

Filename: Session/Session.php

Line Number: 284

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 14
Function: __construct

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: session_set_cookie_params(): Session cookie parameters cannot be changed after headers have already been sent

Filename: Session/Session.php

Line Number: 291

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 14
Function: __construct

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: ini_set(): Session ini settings cannot be changed after headers have already been sent

Filename: Session/Session.php

Line Number: 306

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 14
Function: __construct

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: ini_set(): Session ini settings cannot be changed after headers have already been sent

Filename: Session/Session.php

Line Number: 316

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 14
Function: __construct

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: ini_set(): Session ini settings cannot be changed after headers have already been sent

Filename: Session/Session.php

Line Number: 317

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 14
Function: __construct

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: ini_set(): Session ini settings cannot be changed after headers have already been sent

Filename: Session/Session.php

Line Number: 318

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 14
Function: __construct

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: ini_set(): Session ini settings cannot be changed after headers have already been sent

Filename: Session/Session.php

Line Number: 319

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 14
Function: __construct

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: ini_set(): Session ini settings cannot be changed after headers have already been sent

Filename: Session/Session.php

Line Number: 377

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 14
Function: __construct

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: ini_set(): Session ini settings cannot be changed after headers have already been sent

Filename: drivers/Session_files_driver.php

Line Number: 108

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 14
Function: __construct

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: session_set_save_handler(): Session save handler cannot be changed after headers have already been sent

Filename: Session/Session.php

Line Number: 110

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 14
Function: __construct

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: Warning

Message: session_start(): Session cannot be started after headers have already been sent

Filename: Session/Session.php

Line Number: 143

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 14
Function: __construct

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property Contents::$session is deprecated

Filename: core/Loader.php

Line Number: 1279

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 14
Function: __construct

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property Contents::$agent is deprecated

Filename: core/Loader.php

Line Number: 1279

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 14
Function: __construct

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property Contents::$contentsStatus is deprecated

Filename: libraries/Common.php

Line Number: 64

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 64
Function: _error_handler

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 24
Function: initContentsStatusInfo

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 14
Function: __construct

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property Contents::$articleStatus is deprecated

Filename: libraries/Common.php

Line Number: 71

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 71
Function: _error_handler

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 24
Function: initContentsStatusInfo

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 14
Function: __construct

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property Contents::$db is deprecated

Filename: core/Loader.php

Line Number: 390

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/models/ver3/Contents_model.php
Line: 15
Function: database

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 440
Function: model

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 29
Function: initMenu

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 14
Function: __construct

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property CI_DB_mysqli_driver::$failover is deprecated

Filename: database/DB_driver.php

Line Number: 371

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/models/ver3/Contents_model.php
Line: 15
Function: database

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 440
Function: model

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 29
Function: initMenu

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 14
Function: __construct

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property Contents_model::$best_cnt is deprecated

Filename: ver3/Contents_model.php

Line Number: 17

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/models/ver3/Contents_model.php
Line: 17
Function: _error_handler

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 440
Function: model

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 29
Function: initMenu

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 14
Function: __construct

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property Contents_model::$popular_cnt is deprecated

Filename: ver3/Contents_model.php

Line Number: 18

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/models/ver3/Contents_model.php
Line: 18
Function: _error_handler

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 440
Function: model

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 29
Function: initMenu

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 14
Function: __construct

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property Contents::$member_model is deprecated

Filename: core/Loader.php

Line Number: 353

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/models/ver3/Contents_model.php
Line: 20
Function: model

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 440
Function: model

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 29
Function: initMenu

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 14
Function: __construct

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property Contents::$contents_model is deprecated

Filename: core/Loader.php

Line Number: 353

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 440
Function: model

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 29
Function: initMenu

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 14
Function: __construct

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property Contents::$menuList is deprecated

Filename: libraries/Common.php

Line Number: 561

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 561
Function: _error_handler

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 29
Function: initMenu

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 14
Function: __construct

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property Contents::$common is deprecated

Filename: core/Loader.php

Line Number: 1279

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 14
Function: __construct

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property Contents::$dto is deprecated

Filename: core/Loader.php

Line Number: 1279

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 14
Function: __construct

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property Contents::$together_end_date is deprecated

Filename: ver3/Contents.php

Line Number: 17

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 17
Function: _error_handler

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property CI_Cache::$dummy is deprecated

Filename: libraries/Driver.php

Line Number: 188

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/models/ver3/Contents_model.php
Line: 799
Function: get

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 605
Function: getComment

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 425
Function: initBoardView

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property CI_Loader::$benchmark is deprecated

Filename: core/Loader.php

Line Number: 925

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 387
Function: view

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 557
Function: get_header

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property CI_Loader::$hooks is deprecated

Filename: core/Loader.php

Line Number: 925

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 387
Function: view

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 557
Function: get_header

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property CI_Loader::$config is deprecated

Filename: core/Loader.php

Line Number: 925

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 387
Function: view

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 557
Function: get_header

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property CI_Loader::$log is deprecated

Filename: core/Loader.php

Line Number: 925

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 387
Function: view

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 557
Function: get_header

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property CI_Loader::$utf8 is deprecated

Filename: core/Loader.php

Line Number: 925

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 387
Function: view

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 557
Function: get_header

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property CI_Loader::$uri is deprecated

Filename: core/Loader.php

Line Number: 925

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 387
Function: view

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 557
Function: get_header

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property CI_Loader::$exceptions is deprecated

Filename: core/Loader.php

Line Number: 925

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 387
Function: view

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 557
Function: get_header

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property CI_Loader::$router is deprecated

Filename: core/Loader.php

Line Number: 925

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 387
Function: view

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 557
Function: get_header

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property CI_Loader::$output is deprecated

Filename: core/Loader.php

Line Number: 925

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 387
Function: view

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 557
Function: get_header

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property CI_Loader::$security is deprecated

Filename: core/Loader.php

Line Number: 925

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 387
Function: view

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 557
Function: get_header

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property CI_Loader::$input is deprecated

Filename: core/Loader.php

Line Number: 925

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 387
Function: view

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 557
Function: get_header

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property CI_Loader::$lang is deprecated

Filename: core/Loader.php

Line Number: 925

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 387
Function: view

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 557
Function: get_header

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property CI_Loader::$load is deprecated

Filename: core/Loader.php

Line Number: 925

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 387
Function: view

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 557
Function: get_header

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property CI_Loader::$cache is deprecated

Filename: core/Loader.php

Line Number: 925

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 387
Function: view

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 557
Function: get_header

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property CI_Loader::$cacher is deprecated

Filename: core/Loader.php

Line Number: 925

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 387
Function: view

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 557
Function: get_header

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property CI_Loader::$jscript is deprecated

Filename: core/Loader.php

Line Number: 925

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 387
Function: view

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 557
Function: get_header

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property CI_Loader::$session is deprecated

Filename: core/Loader.php

Line Number: 925

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 387
Function: view

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 557
Function: get_header

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property CI_Loader::$agent is deprecated

Filename: core/Loader.php

Line Number: 925

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 387
Function: view

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 557
Function: get_header

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property CI_Loader::$contentsStatus is deprecated

Filename: core/Loader.php

Line Number: 925

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 387
Function: view

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 557
Function: get_header

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property CI_Loader::$articleStatus is deprecated

Filename: core/Loader.php

Line Number: 925

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 387
Function: view

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 557
Function: get_header

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property CI_Loader::$db is deprecated

Filename: core/Loader.php

Line Number: 925

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 387
Function: view

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 557
Function: get_header

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property CI_Loader::$member_model is deprecated

Filename: core/Loader.php

Line Number: 925

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 387
Function: view

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 557
Function: get_header

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property CI_Loader::$contents_model is deprecated

Filename: core/Loader.php

Line Number: 925

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 387
Function: view

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 557
Function: get_header

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property CI_Loader::$menuList is deprecated

Filename: core/Loader.php

Line Number: 925

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 387
Function: view

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 557
Function: get_header

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property CI_Loader::$common is deprecated

Filename: core/Loader.php

Line Number: 925

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 387
Function: view

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 557
Function: get_header

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property CI_Loader::$dto is deprecated

Filename: core/Loader.php

Line Number: 925

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 387
Function: view

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 557
Function: get_header

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property CI_Loader::$together_end_date is deprecated

Filename: core/Loader.php

Line Number: 925

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 387
Function: view

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 557
Function: get_header

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property Article_model::$best_cnt is deprecated

Filename: ver3/Article_model.php

Line Number: 18

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/models/ver3/Article_model.php
Line: 18
Function: _error_handler

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 322
Function: model

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 392
Function: getFloatingMyInfo

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 559
Function: get_footer

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property Article_model::$popular_cnt is deprecated

Filename: ver3/Article_model.php

Line Number: 19

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/models/ver3/Article_model.php
Line: 19
Function: _error_handler

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 322
Function: model

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 392
Function: getFloatingMyInfo

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 559
Function: get_footer

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property Contents::$article_model is deprecated

Filename: core/Loader.php

Line Number: 353

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 322
Function: model

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 392
Function: getFloatingMyInfo

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 559
Function: get_footer

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

A PHP Error was encountered

Severity: 8192

Message: Creation of dynamic property CI_Loader::$article_model is deprecated

Filename: core/Loader.php

Line Number: 925

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
Line: 434
Function: view

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 559
Function: get_footer

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once

수학동아 - 폴리매스

본문바로가기

주니어 폴리매스 문제

수학 문제를 푸는 매력에 빠져 보세요!

[오일러 프로젝트] 수 퀴즈 온더 블럭: 500개 이상의 약수를 갖는 가장 작은 삼각수는 무엇일까?

수학동아 2020.08.28 01:15 조회 1346

페이스북 트위터 카카오톡 카카오스토리 네이버블로그 네이버밴드

코.알.못 홍 기자의 코딩 도전기

코딩의 ‘코’자도 모르는 코.알.못. 홍 기자가 수학 문제를 코딩으로 푸는 오일러 프로젝트 문제를 하나하나 해결해 나갈 예정입니다. 오일러 프로젝트는 수학과 프로그래밍 실력을 모두 키울 수 있도록 2001년에 만든 수학 문제 웹사이트입니다. 홍 기자와 함께한다면 수학과 파이썬 모두 정복할 수 있지 않을까요?

홍아름 기자와 레온하르트 오일러가 여러분을 미션의 주인공으로 모십니다!

해야 할 미션은 한 가지, 1분 안에 문제의 답을 찾기만 하면 됩니다.

단, 코딩으로만 풀어야 하죠.

수학동아 자기님들! 오일러 프로젝트 문제 한번 풀어보실래요~?

<오일러 프로젝트 12번>

삼각수는 n(n+1)/2 공식으로 구할 수 있어요.

n에 1부터 차례대로 넣으면 다음과 같습니다.

1, 3, 6, 10, 15, 21, 28, 36, 45, 55, …

그렇다면 500개 이상의 약수를 갖는 가장 작은 삼각수는 무엇일까요?

지난 45번 문제에 이어 또 다시 삼각수가 등장했습니다. 삼각수는 말 그대로 삼각형 형태를 만드는 데 필요한 점의 개수로, 1부터 시작한 연속된 자연수의 합이기도 합니다. 이번 12번 문제에서는 삼각수의 약수 개수도 구해야 합니다.

약수는 어떤 수를 나눴을 때 나눠떨어지게 하는 자연수로, 어떤 자연수 n의 약수의 개수는 n보다 작은 자연수로 일일이 나눠보며 찾을 수 있죠. 60의 약수를 한번 찾아볼까요?

이때 1과 60, 2와 30, 3과 20, 4와 15, 5와 12, 6과 10으로 둘씩 짝지어지는 것을 알 수 있습니다. 따라서 60의 경우는 6개의 자연수만 확인해보면 약수의 개수를 찾을 수 있죠. 즉 자연수 n의 약수를 찾을 때 n보다 작은 모든 자연수 대신 √n보다 작거나 같은 자연수로만 나눠보면 약수를 찾을 수 있습니다.

이 방법을 코드로 나타내 12번 문제를 해결해보겠습니다!

파이썬 완전정복! 필수 명령어

1. 약수의 개수를 구하는 함수 만들기

어떤 자연수 n이 √n보다 작은 자연수로 나눠떨어지는지를 보고, 약수의 개수를 찾는 함수 num_factors(n)을 만들겠습니다. 변수 f를 약수의 개수, i를 n을 나눌 수라고 할 때 f와 i 초깃값은 모두 2입니다. 그리고 i를 i²이 n보다 작거나 같을 때까지 1씩 늘려가며 n을 나눠떨어지게 하는지 확인합니다.

2. num_factors(n) 함수로 답 얻기

자연수의 약수의 개수를 찾는 함수에 삼각수를 대입해 답을 찾습니다. 이때 k번째 삼각수를 구하는 식 k(k+1)/2을 이용하는데, 이 식은 1부터 k까지의 자연수를 모두 더한 값을 구하는 공식과 같습니다. 따라서 k번째 삼각수를 구할 때 매번 1부터 k까지의 수들의 합을 구할 필요 없이, k-1번째 삼각수에 k를 더하기만 하면 되죠. 코드에서는 k번째 삼각수 t가 500개보다 작은 약수의 개수를 갖는다면, 그다음 k+1번째 삼각수를 구하기 위해 t에 k+1을 더한 뒤 다시 약수의 개수를 구합니다. 이 과정을 반복해 약수가 500개 이상인 수를 찾으면 while 문에서 나와 정답을 출력합니다.

도전! 오일러 프로젝트 12번 문제 뽀개기

* 코딩 언어는 Python으로 두고 실행하세요!

#1~7 약수의 개수를 얻는 num_factors(n) 함수를 정의합니다.

#8 num_factors(n) 함수를 사용해 오일러 프로젝트 12번 문제의 답을 찾는 함수 e012()를 정의합니다.

#9 삼각수 t의 초깃값은 1이고, 첫 번째 삼각수이므로 순번을 나타내는 k의 초깃값을 1로 둡니다.

#10~11 삼각수 t의 약수의 개수가 500개보다 적다면, t에 k+1을 더해 다음 k+1번째 삼각수를 구하고, while문을 반복합니다.

#12 약수의 개수가 500개 이상이면 while문을 벗어나고, 이때의 t를 돌려줍니다.

#13 함수 e012()를 실행해 답을 얻습니다.

Bonus! 오일러 퀴즈

오일러 프로젝트 12번 문제를 위 코딩창에서 풀어보고, 다음 예제 문제에도 도전해보세요!

① 약수의 개수가 500개 이상인 가장 작은 오각수를 찾아보자.

Hint. n번째 오각수 = n(3n-1)/2

② 소인수분해를 이용해 약수의 개수를 구하는 코드를 만들어보자.

Hint. 어떤 자연수가 a^p×b^q×c^r으로 소인수분해되면, 약수의 개수는 (p+1)(q+1)(r+1)이다.

이번 해답 코드를 이용해 12번 문제의 답을 찾으면 7~8초 정도가 걸립니다. 물론 1분 이내이긴 하지만, 프로 코딩러라면 몇 초 동안 멍하니 기다리는 것도 고역이죠! 삼각수의 성질을 이용해 더 빨리 계산할 수 있는 꿀팁을 알려드릴게요!

----------------------------------------꿀팁 구간----------------------------------------

삼각수를 구하는 식 k(k+1)/2의 식을 보면, 서로소인 두 수 k와 (k+1)의 곱으로 이뤄져있습니다. 만약 k가 짝수라면 k+1은 홀수, 반대로 k가 홀수라면 k+1은 짝수가 되죠. 어느 쪽이건 짝수인 쪽을 2로 나누면 삼각수는 서로소인 두 숫자의 곱으로 나타낼 수 있습니다.

이 서로소인 두 수를 a, b라고 할 때, 삼각수의 약수 개수는 (a의 약수 개수)×(b의 약수 개수)와 같습니다. 따라서 삼각수보다 작은 자연수로 일일이 나눌 필요 없이 삼각수를 이루는 a, b를 구해 각각의 약수 개수를 구하고 곱하면 됩니다. 이 방법을 이용한 것이 아래의 코드로, 얼마나 빨라지는지 한번 실행해보세요!

이전글 수학 (코딩으로) 싹쓰리: 40755보다 큰 삼각수 중에서 오각수와 육각수도 되는 가장 작은 수는?

다음글 수은파 - 수학자들의 은밀한 파티: 10000 이하 모든 친화수의 합은 얼마일까?

문제 찜하기 목록보기

댓글 작성하기

수학 짜장 Lv.5 2020.12.17 20:42

흠....

댓글 작성하기 좋아요0 댓글수0

닫기

지금 바로
로그인해보세요

로그인 하기

로그인 하면 내가 찜한 문제와 수행 평가를 한곳에서 볼 수 있어요!

㈜동아사이언스 | 등록번호 : 서울 아04396 | 등록일자 : 2017년 3월 2일 | 제호 : 동아사이언스 | 발행인 : 장경애 | 편집인 : 김민수
㈜동아사이언스 폴리매스 | 대표 : 장경애 | 개인정보 보호책임자 : 주세훈(privacy@dongascience.com) | 청소년보호책임자 : 박무성
(03737) 서울시 서대문구 충정로 29, 10층 ｜ 문의 : 02-6749-2000 ｜팩스 : 02-3148-0809 ｜사업자등록번호 : 101-81-62201 (사업자정보확인)
통신판매업신고번호 : 제2013-서울용산-01101호 ｜온라인 결제를 위한 PG사의 구매안전서비스(가입사실 확인)

폴리매스 문제는 과학기술진흥기금 및 복권기금의 재원으로 운영되고, 과학기술정보통신부와 한국과학창의재단의 지원을 받아 수행된 성과물로 우리나라의 과학기술 발전과 사회적 가치 증진에 기여하고 있습니다.
☎문의 02-6749-3911