# My 500 followers problem!

Algebra Level 5

$$P(x)=500x^{499}+495x^{498}+490x^{497}+485x^{496} \ldots -1990x-1995$$

Consider the 499th degree polynomial above.

If $$P(2)$$ can be written as $$a+b \times c^d$$ where $$a,b,c,d$$ are positive integers and $$c$$ is not a perfect $$k^{\text{th}}$$ power, find the smallest positive integral value of $$f$$ satisfying $$a + b + c + d \equiv f \pmod{500}$$.

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