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수학동아 - 폴리매스
본문바로가기
함께 풀고 싶은 문제
창의력을 기를 수 있는 수학 문제 또는 퍼즐을 내는 곳입니다.
[창의 퍼즐] 증명하기
K-RIEMANN 2019.03.23 16:16 조회 660

다음을 증명하세요.

x^n=xy

 

 

 

이 문제 어떠셨나요?

글쎄요

0

어려워요

0

  •  
    K-RIEMANN Lv.10 2019.03.23 16:17

    저도 정답을 모르니 공개댓글로 남겨주세요.

    댓글 작성하기 좋아요0 댓글수0
  •  
    디듀우 Lv.7 2019.03.24 03:37

    3^2=3*4면 옳지 않습니다.

    반증 끝!

    댓글 작성하기 좋아요0 댓글수4
    •  
      K-RIEMANN Lv.10 2019.03.24 07:05

      3^2=3X2 입니다

      N과 Y는 같을 수 있다고 칩시다

      좋아요1
    •  
      muse Lv.6 2019.03.24 08:24

      출제자 님께서 무엇을 의도하셨는지 장확히 모르겠네요. 문제의 원문대로 해석하면, 윗 분이 올려주신 반증이 맞습니다.

      제가 유추하기에는, 임의의 자연수 x, n에 대해 저 조건을 민족하는 Y가 존재한다는 것을 증명하는 것 같긴 합니다만, 그러한 경우 문제는 "임의의 자연수 x, n에 대하여 x^n=xy를 만족하는 자연수 y가 존재함을 증명하시오."가 되어야 합니다. 그럼 그냥 y=x^(n-1)이면 됩니다만...

       

      아, 그리고 3^2=3*2는 옳지 않은 식입니다.

      좋아요0
    •  
      디듀우 Lv.7 2019.03.24 19:13

      다시 올려주신 식도 옳지 않습니다.

      좋아요0
    •  
      K-RIEMANN Lv.10 2019.03.24 23:10

      디듀우님이 맞았었군요!

      좋아요0
  •  
    아루키데메스 Lv.5 2019.03.26 07:10

    2^2=2X2

    맞지 않나요??

    댓글 작성하기 좋아요0 댓글수1
    •  
      K-RIEMANN Lv.10 2019.03.26 16:06

      그 식도 맞군요!

      좋아요0
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