수학동아 - 폴리매스

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함께 풀고 싶은 문제

창의력을 기를 수 있는 수학 문제 또는 퍼즐을 내는 곳입니다.

[창의 퍼즐] 최대공약수 집합

△π 2020.04.24 07:52 조회 634

문제 푼 사람 0명

페이스북 트위터 카카오톡 카카오스토리 네이버블로그 네이버밴드

ad는 bc와 같지 않은 양의 정수 a, b, c d가 이며 gcd(a,b,c,d)=1을 만족한다. 모든 양의 정수 n에 대하여 gcd(an+b,cn+d)의 값을 모아 만든 집합을 S라 하자. 집합 S는 어떤 양의 정수의 모든 양의 약수의 집합이 됨을 보여라.

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