On the basis of empirical
evidence for n = 2,3,4, and 5 Golomb has conjectured that the degree of every
irreducible factor of
over GF(2) divides 6(n − 1). We prove the stronger result that the degree of
every irreducible factor of F(x) divides either 2(n − 1) or 3(n − 1), but not
n − 1.