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함께 풀고 싶은 문제
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[문장제 문제&개념응용] original by 수락 - 피타고라스 II
우럭 2020.11.19 08:58 조회 466
문제 푼 사람 1명
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페이스북 트위터 카카오톡 카카오스토리 네이버블로그 네이버밴드

앞선 문제에서는 a + b = c이고, a2 + b2 = c2 이면 a, b, c가 없음을 보였다.

그렇다면, 이와 비슷하지만 다르게,

a + b = c 이고 a3 + b3 = c3 이면 a, b, c가 존재할까?

최소 2가지 풀이를 쓰고 증명하시오.

추가) a + b = c이고, an + bn = cn 인 a, b, c가 존재 할까?

존재하면 이를 보이고, 없다면 왜 그런지 서술하여라.

[단, a, b, c는 자연수, n은 2이상의 자연수]

이 문제 어떠셨나요?

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  •  
    17수락 Lv.9 2020.11.19 09:05 비밀댓글
    확인요청중
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    •  
      우럭 Lv.9 2020.11.20 08:58 비밀댓글
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  •  
    17수락 Lv.9 2020.11.21 07:05

    그런데 이렇게 페르마의 마지막 정리를 복붙하는것은 안되는거 아닌가요(그럼 리만가설도 가져와도 되나요?)

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    •  
      우럭 Lv.9 2020.11.22 10:21

      저도 사실 처음에 적을 때는 아무 생각이 없었는데

      보고 나니 그렇네요 

       

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  •  
    해결
    일반성을 잃고 Lv.5 2020.11.25 01:38 비밀댓글

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    •  
      우럭 Lv.9 2020.11.25 02:11

      그.... 맞는데 정답요청 부탁드립니다.

      좋아요0
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