# Unifying Divisibility

Level pending

Let $$m$$ be the number of integers $$n$$ with $$1 \leq n \leq 2013$$ such that the polynomial $$x^{2n} + 1 + (x+1)^{2n}$$ is divisible by $$x^2 + x + 1$$. Find $$m \pmod {1000}$$.

**Problem credit goes to Artofproblemsolving foundation.

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