Factorization of Fibonacci polynomial – mathoverflow.net

Let $F_N(x)$ be the $N$-th order Fibonacci polynomial over $GF(2)$. I conjecture that $F_{6M+3}(x)=(x^2+1)G^2_1(x)...G^2_K(x)$ where $G_k(x)$ are distinct irreducible factors. Example: ...