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수학동아 - 폴리매스
본문바로가기
함께 풀고 싶은 문제
깊이 고민해볼 수 있는 수학 문제를 내는 곳입니다
[세상을 바꿀 문제] 수로 수 표현하기
바람개비 2021.03.10 21:25 조회 780
문제 푼 사람 0명
공유하기
페이스북 트위터 카카오톡 카카오스토리 네이버블로그 네이버밴드

1보다 크고 서로소인 정수 a, b를 고르자.

임의의 자연수를 a, b로 이루어진 서로 다른 항의 덧셈과 뺄셈으로 표현할 수 있을까?

 

예를 들어 a=2, b=5 이면 3=a^3-b, 19=a^3b+a^2-b^2 으로 나타낼 수 있다.

이 문제 어떠셨나요?

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  •  
    다시 도전
    sicma Lv.11 2021.03.10 23:52 비밀댓글
    비밀 댓글이 등록 되었습니다.
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    •  
      바람개비 Lv.5 2021.03.11 00:32

      앗, 서로소라는 조건을 빠트렸네요...

      그리고 'a, b로 이루어진 항'이란 말은 계수가 모두 1이라는 뜻입니다!

      좋아요0
  •  
    다시 도전
    sicma Lv.11 2021.03.11 03:10 비밀댓글
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    •  
      바람개비 Lv.5 2021.03.11 04:18

      조건 하나 추가했습니다.

      출제는 오랜만이라 실수가 많네요 :(

      좋아요0
  •  
    다시 도전
    로지컬 파이 Lv.4 2021.03.11 17:07 비밀댓글
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    •  
      바람개비 Lv.5 2021.03.11 18:15 비밀댓글
      비밀 댓글이 등록 되었습니다!
    •  
      로지컬 파이 Lv.4 2021.03.11 22:40

      저 따라한거 아닙니다.

      좋아요0
  •  
    PF＿ Lv.8 2021.03.12 00:27

    서로소가 뭐죠?

    댓글 작성하기 좋아요0 댓글수9
    •  
      바람개비 Lv.5 2021.03.12 00:57

      (1, 3), (2, 5, 9), (1, 4, 6, 8) 처럼 공통된 약수가 1밖에 없는 자연수입니다.

      좋아요0
    •  
      천왕 우주선 Lv.5 2021.03.26 21:30

      와..........그걸 모른다고요? 중1-1에 나오는 건데.....

      좋아요0
    •  
      시그마가싫어요 Lv.9 2021.03.27 00:36

      그거 중 1에 나오는건데 그럼 중 1-2도 배웠을리가 없을텐데 그게 2,3학년과도 연결이 되니까... 설마 문제 다 퍼오신건가요? 출처도 안 밝히시고요? 그건 그렇고 어떤 글에 보니까 문제는 다 자작이라고 되있던데 설명좀 부탁드립니다

      @숫자파이

      좋아요0
    •  
      유한의끝도못본남자 Lv.7 2021.03.27 00:48

      모르면 알려줘야지 왜...

      좋아요0
    •  
      PF＿ Lv.8 2021.03.27 01:05

      @SONIC저 초 4인데요?

      @파이파이 @자몽파이 @놀라운-폴리매스 저는 수학을 할 때 막 중 1에서 배우는 기호는 모르고 중3에서 배우는 것은 아는 그런 좀 신기한 사람입니다. (실제)

      좋아요0
    •  
      잡담 Lv.7 2021.03.27 06:34

      @숫자파이

      공부는 차례대로 하세요.... 의심받으니까요

      좋아요0
    •  
      시그마가싫어요 Lv.9 2021.03.27 07:07

      @무한대의끝을본남자

      숫자파이님께서 서로소를 모르시면서 중학교 3학년 문제를 내시니까...

      좋아요0
    •  
      유한의끝도못본남자 Lv.7 2021.03.28 01:21

      @숫자파이

      그런식으로 공부하면 공부가 되지않아요

       

      실제로 숫파님처럼 해봤던 사람입니다...

      지금은 물론 기초가 단단히 잡혔지만 조언입니다

      좋아요0
    •  
      PF＿ Lv.8 2021.03.28 02:09

      @무한대의끝을본남자

      알겠습니다^^

      잘 활용하겠습니다^^

      좋아요0
  •  
    다시 도전
    로지컬 파이 Lv.4 2021.03.13 23:19 비밀댓글
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    •  
      바람개비 Lv.5 2021.03.14 18:27

      이 문제는 자연수가 오직 항의 합차만으로 표현될 수 있는지 묻는 문제입니다.

      로그나 제곱근 등의 다른 수학 개념을 쓰면 안돼요.

      좋아요0
  •  
    로지컬 파이 Lv.4 2021.03.14 18:44 비밀댓글
    확인요청중
    비밀 댓글이 등록 되었습니다.
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    •  
      바람개비 Lv.5 2021.03.14 18:59 비밀댓글
      비밀 댓글이 등록 되었습니다!
  •  
    다시 도전
    로지컬 파이 Lv.4 2021.03.14 18:44 비밀댓글
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    •  
      로지컬 파이 Lv.4 2021.03.14 18:45

      죄송해요 렉이 걸려서 똑같은거 2개 보냈네요.

      정답확인은 하나만 해주세요.

      좋아요1
  •  
    Amath Lv.8 2021.05.15 04:11

    한 a, b의 합과 차로 모든 자연수를 표현할 수 있다는 걸 증명하란 문제인가요?

    댓글 작성하기 좋아요0 댓글수1
    •  
      바람개비 Lv.5 2021.05.27 08:39

      네, 정확히는 an 또는 bm, 혹은 anbm 형태의 식(n, m은 자연수)의 합차로 표현 가능한지 증명하시면 돼요.

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