Determine all sequences of positive integers, such that for every positive integer there exists an integer with
Proposed by Warut Suksompong, Thailand
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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
Izvor: Međunarodna matematička olimpijada, shortlist 2011
Školjka 
of positive integers, such that for every positive integer 
there exists an integer 
with 