# How Can I Solve It!!

Determine all sequences $$(x_{1},....,x_{2011})$$ of positive integers such for every positive integer $$n$$ there is an integer a with

$$x_{1}^{n}+2x_{2}^{n}+....+2011x_{2011}^{n}=a^{n+1}+1$$.

Find the sum of all of the entries of all of the sequences.

Note: Suppose the solutions are $$(1,2,3...,2011)$$ and$$(2,4,6,8,...,4022)$$, then your answer will be $$1+2+3+...+2011+2+4+6+....+4022=6069198$$

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