# Wow!

Algebra Level pending

Define a Geber rotation to be the swapping of coefficient $$k$$ with $$n+1-k$$ in an $$n^\text{th}$$ degree polynomial. Find the number of integer rooted $$2016^\text{th}$$ degree polynomials such that roots are not changed when coefficients are changed in a Geber rotation and let this be $$k$$. Find the remainder of $$k$$ when divided by 1000.

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