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IMO Shortlist 2011, Algebra 2

Source: IMO Shortlist 2011, Algebra 2

July 11, 2012

algebraIMO ShortlistequationSequence

Problem Statement

Determine all sequences

(x_1,x_2,\ldots,x_{2011})

of positive integers, such that for every positive integer

n

there exists an integer

a

with

\sum^{2011}_{j=1} j x^n_j = a^{n+1} + 1

Proposed by Warut Suksompong, Thailand