# Alternating Exponential Prime Finite Sum Polynomial (n=7)

Number Theory Level pending

Let $$s_7(x)=7x^7+a_6x^6+a_5x^5-7^5x^4+7^4x^3-7^3x^2+7^2x-7$$. Find $$a_6$$ and $$a_5$$ such that $$x=-\frac{1}{7}$$ is a rational root and the sum of the coefficients is $$2(1+2+3+4+5+6+7)$$.

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