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[창의 퍼즐] [대수]무리수를 정수로 만들 수 있을까?

mwryan 2020.09.03 19:10 조회 509

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$r=a+b \sqrt{c}$ (단, a, b, c는 모두 양의 정수)꼴의 무리수 r이 있다. 모든 자연수 n에 대해, $r^n +s^n$ 가 항상 정수가 되도록 하는 무리수 s가 항상 유일한가?

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222 Lv.9 2020.09.03 20:03 비밀댓글

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- mwryan Lv.6 2020.09.03 21:00 비밀댓글
  
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베네딕트0724 Lv.6 2020.09.03 20:54 비밀댓글

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- mwryan Lv.6 2020.09.03 20:59 비밀댓글
  
  비밀 댓글이 등록 되었습니다!
- 베네딕트0724 Lv.6 2020.09.07 00:20
  
  아하 문제 이해를 잘못 했네요. 그러니까 문제 뜻은 $r=a+b \sqrt{c}$ (단, a, b, c는 모두 양의 정수)꼴의 무리수 r에 대해 무리수 s가 유일하게 존재하여, 모든 자연수 n에 대해 $r^n +s^n$ 가 항상 정수가 되게 하는가?
  
  라고 이해하면 될까요
  
  좋아요0