Unlucky Polynomial
Algebra
Level
5
Suppose \(f(x)\) is a polynomial of degree \(13\) that satisfies the functional equation \[f(2x^2-1)=2(f(x))^2-1\] Find the last three digits of the coefficient of \(x^5\) in \(f\).
Details and assumptions
The coefficient of \(x^5\) is a positive integer.
by
Calvin Lin