Teorema 6. Pentru p > 0, numar prim, avem:p (X) = Xp-1+ Xp-2 + + X + 1. (10)

Exemple. Primele 10 polinoame ciclotomice:1 (X) = X 12 (X) = X + 13 (X) = X2 + X + 14 (X) = X2 + 15 (X) = X4 + X3 + X2 + X + 16 (X) = X2 X + 17 (X) = X6 + X5 + X4 + X3 + X2 + X + 18 (X) = X4 + 19 (X) = X6 + X3 + 110 (X) = X4 X3 + X2 X + 1.