# 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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