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 Article::$benchmark is deprecated

Filename: core/Controller.php

Line Number: 75

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Article.php
Line: 12
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 Article::$hooks is deprecated

Filename: core/Controller.php

Line Number: 75

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Article.php
Line: 12
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 Article::$config is deprecated

Filename: core/Controller.php

Line Number: 75

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Article.php
Line: 12
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 Article::$log is deprecated

Filename: core/Controller.php

Line Number: 75

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Article.php
Line: 12
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 Article::$utf8 is deprecated

Filename: core/Controller.php

Line Number: 75

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Article.php
Line: 12
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 Article::$uri is deprecated

Filename: core/Controller.php

Line Number: 75

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Article.php
Line: 12
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 Article::$exceptions is deprecated

Filename: core/Controller.php

Line Number: 75

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Article.php
Line: 12
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 Article::$router is deprecated

Filename: core/Controller.php

Line Number: 75

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Article.php
Line: 12
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 Article::$output is deprecated

Filename: core/Controller.php

Line Number: 75

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Article.php
Line: 12
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 Article::$security is deprecated

Filename: core/Controller.php

Line Number: 75

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Article.php
Line: 12
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 Article::$input is deprecated

Filename: core/Controller.php

Line Number: 75

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Article.php
Line: 12
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 Article::$lang is deprecated

Filename: core/Controller.php

Line Number: 75

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Article.php
Line: 12
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 Article::$load is deprecated

Filename: core/Controller.php

Line Number: 78

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Article.php
Line: 12
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/Article.php
Line: 12
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/Article.php
Line: 12
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 Article::$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/Article.php
Line: 12
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 Article::$cacher is deprecated

Filename: core/Loader.php

Line Number: 1279

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Article.php
Line: 12
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 Article::$jscript is deprecated

Filename: core/Loader.php

Line Number: 1279

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Article.php
Line: 12
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/Article.php
Line: 12
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/Article.php
Line: 12
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/Article.php
Line: 12
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/Article.php
Line: 12
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/Article.php
Line: 12
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/Article.php
Line: 12
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/Article.php
Line: 12
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/Article.php
Line: 12
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/Article.php
Line: 12
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/Article.php
Line: 12
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/Article.php
Line: 12
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/Article.php
Line: 12
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/Article.php
Line: 12
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/Article.php
Line: 12
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/Article.php
Line: 12
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/Article.php
Line: 12
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/Article.php
Line: 12
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 Article::$session is deprecated

Filename: core/Loader.php

Line Number: 1279

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Article.php
Line: 12
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 Article::$agent is deprecated

Filename: core/Loader.php

Line Number: 1279

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Article.php
Line: 12
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 Article::$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/Article.php
Line: 12
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 Article::$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/Article.php
Line: 12
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 Article::$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/Article.php
Line: 12
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/Article.php
Line: 12
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/Article.php
Line: 12
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/Article.php
Line: 12
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 Article::$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/Article.php
Line: 12
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 Article::$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/Article.php
Line: 12
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 Article::$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/Article.php
Line: 12
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 Article::$common is deprecated

Filename: core/Loader.php

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Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Article.php
Line: 12
Function: __construct

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

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Filename: core/Loader.php

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Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Article.php
Line: 12
Function: __construct

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

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Filename: ver3/Article_model.php

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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/controllers/ver3/Article.php
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Function: model

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Line: 315
Function: require_once

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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/controllers/ver3/Article.php
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Function: model

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Line: 315
Function: require_once

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Filename: core/Loader.php

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File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Article.php
Line: 13
Function: model

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Filename: ver3/Member_model.php

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Line: 279
Function: urldecode

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Article.php
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Function: require_once

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File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Article.php
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Function: require_once

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Line: 674
Function: get

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Article.php
Line: 266
Function: getComment

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Article.php
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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/Article.php
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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/Article.php
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Line: 315
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Filename: core/Loader.php

Line Number: 925

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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/Article.php
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Line: 315
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Filename: core/Loader.php

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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/Article.php
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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/Article.php
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Line: 315
Function: require_once

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Filename: core/Loader.php

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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/Article.php
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Line: 315
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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/Article.php
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Function: get_header

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Line: 315
Function: require_once

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Filename: core/Loader.php

Line Number: 925

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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/Article.php
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Function: get_header

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Line: 315
Function: require_once

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Filename: core/Loader.php

Line Number: 925

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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/Article.php
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Filename: core/Loader.php

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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/Article.php
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Line: 315
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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/Article.php
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Function: get_header

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

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Filename: core/Loader.php

Line Number: 925

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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/Article.php
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Function: get_header

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

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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/Article.php
Line: 220
Function: get_header

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

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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/Article.php
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Function: get_header

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

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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/Article.php
Line: 220
Function: get_header

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

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Severity: 8192

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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/Article.php
Line: 220
Function: get_header

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

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Severity: 8192

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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/Article.php
Line: 220
Function: get_header

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

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Filename: core/Loader.php

Line Number: 925

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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/Article.php
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Function: get_header

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

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Filename: core/Loader.php

Line Number: 925

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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/Article.php
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Function: get_header

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

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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/Article.php
Line: 220
Function: get_header

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

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Severity: 8192

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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/Article.php
Line: 220
Function: get_header

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

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Severity: 8192

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Filename: core/Loader.php

Line Number: 925

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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/Article.php
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Function: get_header

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Line: 315
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Filename: core/Loader.php

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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/Article.php
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Line: 315
Function: require_once

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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/Article.php
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Function: get_header

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Line: 315
Function: require_once

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

Filename: core/Loader.php

Line Number: 925

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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/Article.php
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Function: get_header

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Line: 315
Function: require_once

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Filename: core/Loader.php

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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/Article.php
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Line: 315
Function: require_once

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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/Article.php
Line: 220
Function: get_header

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

자유 기사 기사 작성법
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로보카폴리 2020.05.09 20:10

여러분들께 문제를 하나 내겠습니다.

당신에게는 x개의 사과와 21x^2-12x+1개의 바나나가 있습니다.

이때, 당신은 최대한 많은 사람들에게 공평하게 사과와 바나나를 나누어 줄때,

최대 몇명에게 나누어 줄 수 있을까요?

(한번 생각해보세요, 기사를 다 읽으시고 답을 아시면 댓글로 적어주세요)

 

우리는 이 문제를 풀기 위해, 최대공약수를 사용합니다..

 

그런데 여러분은 최대공약수가 무엇인지 아시나요?

최대공약수란 공통인 약수중 가장 큰 수를 의미합니다.

 

이때 두 수 a,b 의 최대공약수를 gcd(a,b)라고 하는데요,

예를들어 6과 8의 최대공약수인 gcd(6,8)는 2겠죠?

 

그런데 6,8처럼 작은 수들의 최대공약수는 간단할 수 있겠지만

예를 들어 3142342341234126와 3412342342342의 최대공약수를

구하는 것은 어렵고 시간도 많이 들 것입니다.

 

그렇다면 최대공약수를 쉽고 빠르게 구하는 방법은 없을까요?

 

우리는 두수의 최대공약수를 빠르게 구하기 위해서

"유클리드 호제법"이라는 것을 사용합니다.

 

유클리드 호제법의 핵심은

a,b의 최대공약수는 

a와 b를 a로 나눈 나머지의 최대공약수와 같다는 것인데요,

이를 증명할 수 있습니다.

 

gcd(a,b)=d라 하고 gcd(a,b-a)=e라 하면

a=dx, b=dy, (x,y)=1

그러면, d|d(x-y)=a-b, d|b이므로 d는 a-b, b의 공약수 ->d|e

한편, e|a-b+b=a, e|b이므로 e는 a, b의 공약수->e|d

따라서 d=e

 

위 증명에 의해

a,b의 최대공약수는 a,b-a의 최대공약수와 같고

이를 반복하면 gcd(a,b)=gcd(a,b를 a로 나눈 나머지)임을 알 수 있습니다.

이제 우리는 최대공약수를 쉽고 빠르게 구할 수 있는 무기를 가지고 있습니다.

 

그렇다면 본격적으로 다항식들의 최대공약수를 구해볼까요?

한번 x+1과 x^2+2x+2의 최대공약수를 구해볼까요?

 

x^2+2x+2를 x+1로 나눈 나머지는

x^2+2x+2=(x+1)^2+1임으로

1입니다.

따라서 gcd(x+1,x^2+2x+2)=gcd(x+1,1)=1 입니다.

 

 

다시 말해 x값이 무엇이든

두수는 서로소라는 것이죠(서로소는 최대공약수가 1인

두 수를 말합니다)

 

이제 어떤 두 수나 두 방정식이 나왔을때,

최대공약수를 구하는 방법을 아시겠죠?

A PHP Error was encountered

Severity: Warning

Message: Undefined variable $tag_news_list

Filename: inc/article_view.php

Line Number: 90

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/views/ver3/inc/article_view.php
Line: 90
Function: _error_handler

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Article.php
Line: 221
Function: view

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

A PHP Error was encountered

Severity: Warning

Message: Cannot modify header information - headers already sent by (output started at /volume1/web/PhpstormProjects/www_polymath_co_kr/system/core/Exceptions.php:271)

Filename: core/Common.php

Line Number: 570

Backtrace:

An uncaught Exception was encountered

Type: TypeError

Message: count(): Argument #1 ($value) must be of type Countable|array, null given

Filename: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/views/ver3/inc/article_view.php

Line Number: 90

Backtrace:

File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Article.php
Line: 221
Function: view

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