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수학동아 - 폴리매스
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[잡담] 시즌1 15B 가이드.
화이트가드 2022.01.19 01:45 조회 296
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페이스북 트위터 카카오톡 카카오스토리 네이버블로그 네이버밴드

고등학교 수학으로 충분합니다.

a^2 + b^2  >= 2ab임은 알고 계실것이고,

조건을 잘 생각하시면 a^2 + b^2 = kab일 때, k는 자연수여야 합니다. (그 이유를 생각해보아요)

이 때, a^2 - kba + b^2 = 0이 양의 정수해를 가지려면 판별식 D가 완전제곱이어야 하고... 

 

띠라서 k = ....

대입해서 a,b 조건에 대해서 생각해보면... 

따라서 대입하고, (n에 대한 분수식이 정수가 되려면...) ..... n은 이것뿐이다.

라는 논리로 가시면 편하게 가실 수 있습니다. 

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