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Function: driver
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Function: require_once
수학동아 - 폴리매스
함께 풀고 싶은 문제
창의력을 기를 수 있는 수학 문제 또는 퍼즐을 내는 곳입니다.
아엘
2020.07.28 04:32
조회 554
다음은 모든 자연수 n에 대하여 n^2+2n+12는 121의 배수가 아님을 증명하는 것이다.
n^2+2n+12가 121의 배수라고 가정하면 적당한 자연수 k에 대하여
n^2+2n+12=121k
이 식을 변형하면
(n=1)^2=11(가) ......ㄱ
이므로 (n+1)^2은 11의 배수이다.
n+1=11s (s는 자연수)로 놓고 ㄱ에 대입하면
11(k-s^2)=(나)
이므로 (나)가 11의 배수가 되어 모순이다.
따라서 n^2+2n+12는 121의 배수가 아니다.
위의 증명에서 (가)에 알맞은 식을 f(k), (나)에 알맞은 값을 a라고 할 때, f(a)의 값을 구하여라...
(하....힘들었다..)
풀이는 필수!
-
아엘
Lv.7
2020.07.28 04:32
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