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_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 CI_Cache::$dummy is deprecated
Filename: libraries/Driver.php
Line Number: 188
Backtrace:
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/models/ver3/Contents_model.php
Line: 799
Function: get
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 605
Function: getComment
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
Line: 425
Function: initBoardView
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
Line: 315
Function: require_once
A PHP Error was encountered
Severity: 8192
Message: Creation of dynamic property Article_model::$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
수학동아 - 폴리매스
함께 풀고 싶은 문제
나도 수학쌤 문장제 문제를 변형해 문제를 내는 곳입니다.
sicma
2021.05.11 00:09
조회 452
c가 빗변인 직각삼각형의 세 변을 a,b,c라 하면 a²+b²=c² 가 성립한다.
이때 gcd(a,b,c)=1이면 원시 피타고라스 쌍이라 한다.
1. a,b에는 3의 배수가 있다.
2. a,b,c에는 5의 배수가 있다.
3. a,b에는 4의 배수가 있다.
이를 증명해보자.
또한 그냥 피타고라스 순서쌍을 보자
3이상의 수들은 모두 피타고라스 순서쌍에 포함되는가?
아니라면 어떤 반례가 있는지 들어보고 아니라면 증명해보자.
피타고라스를 입체로 접근해보자
직육면체에서 a를 가로 b를 세로 c를 높이라 하고 d를 빗변으로 한다면
a²+b²+c²=d²와 같이 구할 수 있다.
그렇다면 여기서 gcd(a,b,c,d)=1이라면 위의 1,2,3의 내용이 그대로 적용되는가?
그리고 순서쌍이 많다고 보장할 수 있을까?
이제 제곱수들의 합이 제곱수가 된다고 하자.
a²+b²+...=k²이다. 이것 역시 자연수 해가 무한한가?
그렇다면 세제곱수 k개 더했을 때를 생각해보자.
이때도 만약 제곱수가 나온다고 하자. 그렇다면
k가 어떤수이든 자연수해가 나온다는 걸 보장할 수 있는가?
-
피카파이
Lv.8
2021.05.30 00:43
비밀댓글
비밀 댓글이 등록 되었습니다.
-
sicma
Lv.11
2021.05.30 08:17
비밀댓글
비밀 댓글이 등록 되었습니다!
-
피카파이
Lv.8
2021.05.30 21:19
좋아요0
-
JM
Lv.6
2021.06.18 02:03
비밀댓글
비밀 댓글이 등록 되었습니다.
-
sicma
Lv.11
2021.06.18 10:04
비밀댓글
비밀 댓글이 등록 되었습니다!
지금 바로
로그인해보세요
로그인 하면 내가 찜한 문제와 수행 평가를 한곳에서 볼 수 있어요!
