Solution: 2011-6 Equal sums

Let \(a_1\le a_2\le \cdots \le a_k\) and \(b_1\le b_2\le \cdots \le b_l\) be sequences of positive integers at most M. Prove that if \[ \sum_{i=1}^{k} a_i^n = \sum_{j=1}^l b_j^n\] for all \(1\le n\le M\), then \(k=l\) and \(a_i=b_i\) for all \(1\le i\le k\).

The best solution was submitted by Cho, Yonghwa (조용화), 수리과학과 석사과정 2010학번.

Here is his Solution of Problem 2011-6.

Alternative solutions were submitted by 김지원 (2010학번, +3), 이재석 (수리과학과 2007학번, +3), 구도완 (해운대고등학교 3학년, +3). One incorrect solution was submitted.


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1 thought on “Solution: 2011-6 Equal sums

  1. 익명

    잘못된 풀이는 제꺼 같네요.
    저는 k, l 이 M과 같거나 보다 작다고 놓고 풀었는데
    an, bn의 값이 M보다 작다는 거였네요. ㅠㅠ

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