ISL 2011 A2

Answer

Determine all sequences $\left(x_{1}, x_{2}, \ldots, x_{2011}\right)$ of positive integers such that for every positive integer $n$ there is an integer $a$ with $x_{1}^{n}+2 x_{2}^{n}+\cdots+2011 x_{2011}^{n}=a^{n+1}+1 .$

Dataset text NuminaMath olympiads. Quoted with source.

Official text: IMO 2011 Shortlist booklet, page 5.

Show the answer

(1, k, \ldots, k) \text{ with } k=2023065

Solutions

Official solution Solution 1 by the IMO Problem Selection Committee

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