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Determine all sequences $(y_1, y_2, . . . , y_{2011})$ of positive integers such that for every positive integer $n$ there exist an integer a with $y^n_1 + 2y^n_2 + · · · + 2011y^n_{2011} = a^{n+1}+1$.

Attempts: I have found a sequence $(1,r,r,...)$ where $r=2+...+2011$ satisfies the above equality but i am not sure how to find all the sequence or there is only finitely many.

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Is this a competition problem from 2011? It is very common in competitions to give problems involving the current year. –  Harald Hanche-Olsen Jan 17 '13 at 9:52
    
@HaraldHanche-Olsen I am not sure. This is a question from my friend. –  user56876 Jan 17 '13 at 10:07

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