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

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

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

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

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

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

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

수학동아 - 폴리매스
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[잡담] 수학대소동 책을 보고...
△π 2020.07.11 16:26 조회 535
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페이스북 트위터 카카오톡 카카오스토리 네이버블로그 네이버밴드

정말 흥미로운 책이였어요!

몰입감이 정말 짱이었고, 책이 끝나가는지 모르는 그런 책이었습니다!

그런데, 책을 보다가 궁금한 점이 생겼습니다.

책에서 이런 문제가 있었거든요.

'제곱수와 세제곱수 사이에 낀 수는 26뿐이다'

실제로 이게 맞는지 증명해보고 싶었습니다.

일단 이 문제를 이렇게 변형시켰습니다.

 

|x^3-y^2|=2를 만족하는 자연수 x,y는 x=3, y=5가 유일하다.

 

우선, 이걸 보고 x,y 둘 중 어느것에도 짝수는 들어올 수 없다는 것을 알았습니다.

x^3=y^2+-2이니까요.

x,y의 홀짝성이 다르다면 자명하게 위 식은 성립하지 않고,

x,y가 모두 짝수라면 좌변은 8의배수이나 우변은 4의 배수가 되지 않아 성립하지 않습니다.

그래서 x,y 모두 홀수라는 점을 알아냈습니다.

그 다음부터 막히네요ㅠ

저도 계속 연구해볼테니 혹시 답을 아시는 분은 힌트 주실 수 있나요?

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