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함께 풀고 싶은 문제
창의력을 기를 수 있는 수학 문제 또는 퍼즐을 내는 곳입니다.
[창의 퍼즐] [정수]비둘기 수
Mata 2020.07.15 08:44 조회 1343
문제 푼 사람 1명
공유하기
페이스북 트위터 카카오톡 카카오스토리 네이버블로그 네이버밴드

모든 자릿수가 9로만 이루어진 수를 "비둘기 수"라고 하자. 예를 들자면 9, 99, 9999, 9999999 등이 있다. 이때, 다음 물음에 답하여라.

 

임의의 10과 서로소인 자연수 a와 곱하면 "비둘기 수"가 되는 적당한 자연수 b가 항상 있음을 보여라. 또한 이때 b의 값을 구하는 방법을 쓰고 이를 증명하여라.

이 문제 어떠셨나요?

글쎄요

1

어려워요

1

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  •  
    해결
    mwryan Lv.6 2020.07.15 18:07 비밀댓글

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    비밀 댓글이 등록 되었습니다.
    댓글 작성하기 댓글수1
    •  
      Mata Lv.6 2020.07.15 21:59 비밀댓글
      비밀 댓글이 등록 되었습니다!
  •  
    △π Lv.9 2020.10.25 15:02

    어! 저도 이거랑 아예 똑같은 생각을 한 적 있었는데(순환소수는 유리수임을 증명)

    b의 값을 구하는 방법까지는 생각을 안해봤네요

    댓글 작성하기 좋아요0 댓글수1
    •  
      Mata Lv.6 2020.12.08 04:53

      본 명제를 증명하셨다면 b가 무슨 값이고 또 그것이 왜 그런지도 쉽게 증명이 됩니다!

      좋아요0
  •  
    다시 도전
    73 Lv.4 2021.02.04 01:24 비밀댓글
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    •  
      Mata Lv.6 2021.03.03 10:30 비밀댓글
      비밀 댓글이 등록 되었습니다!
  •  
    다시 도전
    피자 Lv.5 2021.02.12 18:16 비밀댓글
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  •  
    다시 도전
    수학싫은데좋아요 Lv.5 2021.03.01 02:58 비밀댓글
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    •  
      Mata Lv.6 2021.03.03 10:31 비밀댓글
      비밀 댓글이 등록 되었습니다!
    •  
      수학싫은데좋아요 Lv.5 2021.03.05 05:21

      아 그래요?? 그럼 답을 더 찾아봐야겠군요(인터넷에서 검색한다는 말 아님)

      좋아요0

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