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함께 풀고 싶은 문제

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[창의 퍼즐] 페르마 수에 관한 문제

Euler 2018.08.10 06:57 조회 952

문제 푼 사람 0명

페이스북 트위터 카카오톡 카카오스토리 네이버블로그 네이버밴드

이 문제는 수학동아에 나옵니다. 답은 저도 모릅니다.

a번째 페르마 수부터는 페르마 수가 모두 합성수가 된다. 그 a가 존재하는가? 존재한다면 값을 구하시오.

이전글 필즈상 수상자

다음글 소수판정식

이 문제 어떠셨나요?

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파인만 Lv.1 2018.08.10 22:41

페르마 수가 뭐죠?

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- Euler Lv.1 2018.08.11 01:11
  
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  $2^{2^{n}}+1$ 꼴의 수를 말합니다.
  
  좋아요1
파인만 Lv.1 2018.08.11 01:55

여기까지 식을 만들어 봤는데 이식을 이용해 n에대한 xy의 식을 만들면 n이 얼마일 때부터 두 일이 아닌 정수 x, y가 성립하는지 부정 방정식으로 알수 있을 것 같아요!

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- 여백 패르마 Lv.5 2018.08.11 18:26
  
  아니 페르마 수(ㅋㅋ 제 닉네임과 연관이 있네요...) 는 2^(2^n) 형태의 수이지 2^(2n) 형태의 수가 아닙니다.
  
  좋아요1
매쓰콜이야 Lv.1 2018.08.21 08:59

컴퓨터로 해 봤는데, 단순 long long 범위로는 안 되네요. 2⁶³-1이 long long의 최대인데 n이 8이상이면, 컴퓨터가 오류 나요. 컴퓨터로는 안 되나봐요.

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서러서차 Lv.1 2018.08.21 10:11

근데 이 문제 어디선가 본 것 같아서 얘기를 합니다...

현재 n=33일때 까지는 모두 합성수라는 것이 증명되었어요

n=13일때 까지는 모든 소인수가 구해졌고 나머지는 5개~1개까지 천차만별인 걸로 알고 있어요

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