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 \(1\le i\le k\).

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4 thoughts on “2011-6 Equal sums

  1. 익명

    ‘at most M’ 을 어떻게 해석하면 되나요?ㅠㅠ
    k와 l이 M 이하라고 해석하면 될까요?

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