12.2.61 Number theory
Condition: For the polynomial \[ P(x)=\left(x^{3}+x^{2}-1\right)^{2008}\left(x^{2}-x-1\right)^{2009} \] find the sum of the coefficients for even and odd powers \( x\).
A huge number of interesting olympiad problems in number theory, and its various sections.