수학동아 - 폴리매스

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함께 풀고 싶은 문제

창의력을 기를 수 있는 수학 문제 또는 퍼즐을 내는 곳입니다.

[창의 퍼즐] [대수] 전설적인 IMO 문제

△π 2020.08.04 18:11 조회 712

문제 푼 사람 1명

페이스북 트위터 카카오톡 카카오스토리 네이버블로그 네이버밴드

양의 정수 a,b에 대해 $\frac{a^2+b^2}{ab+1}$ 이 정수라면, 이 값은 완전제곱수임을 보여라.

힌트:이 문제로 새로운 기법이 생겼죠... 비에타 점핑이라는 기법!

이전글 [기하, 대수처럼 보이지만 풀어보면...] 포물선 위의 정사각형

다음글 [정수] 파이의 수

이 문제 어떠셨나요?

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도전

대한미국남자 Lv.6 2020.08.04 23:27 비밀댓글

비밀 댓글이 등록 되었습니다.

댓글 작성하기 댓글수3
- 대한미국남자 Lv.6 2020.08.04 23:27
  
  휴 45분 걸렸네요 ㅠㅠ
  
  좋아요0
- infinitepi Lv.9 2020.08.04 23:41
  
  맞으면 대박
  
  좋아요0
- △π Lv.9 2020.08.05 00:51 비밀댓글
  
  비밀 댓글이 등록 되었습니다!

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