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수학동아 - 폴리매스
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[잡담] 수소폭탄으로 개미잡는법
Sagan 2020.10.17 00:25 조회 524
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페이스북 트위터 카카오톡 카카오스토리 네이버블로그 네이버밴드

함풀문에 내기 좀 뭐해서 여기에 써봅니다.

2의 세제곱근이 무리수라는 것을 증명하시오.

2의 세제곱근이 유리수라면 p/q 의 형태로 나타낼 수 있다(p, q는 서로소)

q를 이항하고 양변을 세제곱하면

2q^3=p^3

q^3+q^3=p^3

페르마의 마지막 정리에 의해 위 식을 만족하는 p, q는 존재하지 않는다.

따라서 2의 세제곱근은 무리수이다.

 

Q.E.D(Quod Erat Demonstrandum)

끝

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