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수학동아 - 폴리매스
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[문장제 문제&개념응용] [정수] 문제모음 #2
Plum 2020.12.07 23:02 조회 359
문제 푼 사람 1명
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페이스북 트위터 카카오톡 카카오스토리 네이버블로그 네이버밴드

1. 3이상의 자연수 n에 대해, n²을 2006으로 나눴더니 나머지가 4였다. n의 최솟값을 구해라.

 

2. 9자리의 자연수가 있다. 이 9자리수를 앞에서 부터 3자리씩 끊으면 3자리수 3개가 나온다. 처음 세자리는 끝 세자리수와 같고, 처음세자리수를 2배하니,가운데 세자리 수가 나왔다. 예) 124248124 , 389778389 ..그리고 이 9자리수가 서로 다른 다섯개의 소수의 제곱이 된다. {예) 17²×19²×2²×37²×11² 처럼 소수의 제곱형태가 된다}. 이러한 조건을 모두 만족하는 9자리 자연수의 합을 A라고 하자. A를 100으로 나눈 나머지를 구해라.

 

3. y^{3}=8x^{6}+2x^{3}y-y^{2} 의 정수해 (x,y)를 모두 구해라.

 

(풀이 필수, 1개풀면 해결하나 다풀면 해결 2개)

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    Plum Lv.7 2020.12.07 23:05 비밀댓글
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    여백페르마 Lv.4 2020.12.08 23:18 비밀댓글
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      Plum Lv.7 2020.12.09 00:25 비밀댓글
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