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.
