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 \(a + b + c + d \equiv f \pmod{500}\).

×

Problem Loading...

Note Loading...

Set Loading...