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Let $F_N(x)$ be the $N$-th order Fibonacci polynomial in 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: $F_{15}(x)=(x^2+1)(x^2+x+1)^2(x^4+x^3+1)^2$
I tried to prove it but made no progress. I also looked at some literature:...

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