Question

dealing with functional equations

Answer 1

find all polynomials such that \(p(x^2) = p(x) p(x+1)\) if I recall correctly

Answer 2

\(p(x) = x(x-1)\) is one solution, not sure if there are any others..

Answer 3

Haha yeah, found p(x) = 0 and that one. How to prove that others don't exist?

Answer 4

power series

Answer 5

\(a=a*a \implies a=0\lor 1\)
so \(p(x)=0\) and \(p(x)=1\) are the only constant polynomial solutions

Answer 6

\[\sum_{n=0}^\infty a_nx^{2n} = \sum_{m=0}^\infty\sum_{n=0}^\infty \sum_{k=0}^n a_ma_n \binom{n}{k} x^{m+k}\]

uhhhhhidk