Problem

Source: IMO Shortlist 2011, Algebra 2

Tags: algebra, IMO Shortlist, equation, Sequence



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