Hello. I have big problem with this quest:
Find all polynomials F(x), that answers equation
F(x^2-2x) = F^2 (x-2)
Be detail, please and sorry for ENG.
F(y) = \sum_n a^n y^n[/tex]
So
$\displaystyle F(x^2 - 2x) = \sum_n a_n(x^2 - 2x)^n = a_0 + a_1(x^2 - 2x) + ~... $
We also have
$\displaystyle \left [ F(x^2 - 2x \right ] ^2 = \sum_m \sum _n a_m a_n (x^2 - 2x)^{m + n}$
Work out some terms for the F squared series and compare them.
-Dan