Kreisteilungspolynom/Zerlegung mod p/Tabelle

Die folgende Tabelle zeigt die Primfaktorzerlegung der (über ${}\mathbb {Z}$ und ${}\mathbb {Q}$ irreduziblen) Kreisteilungspolynome ${}\Phi _{n}$ in ${}\mathbb {Z} /(p)[X]$ für die ersten Primzahlen ${}p=2,3,5,7,11,13$.

n	${}\Phi _{n}$	2	3	5	7	11	13
1	${}X-1$	${}X-1$	${}X-1$	${}X-1$	${}X-1$	${}X-1$	${}X-1$
2	${}X+1$	${}X+1$	${}X+1$	${}X+1$	${}X+1$	${}X+1$	${}X+1$
3	${}X^{2}+X+1$	${}X^{2}+X+1$	${}(X+2)^{2}$	${}X^{2}+X+1$	${}(X+5)(X+3)$	${}X^{2}+X+1$	${}(X+10)(X+4)$
4	${}X^{2}+1$	${}(X+1)^{2}$	${}X^{2}+1$	${}(X+2)(X+3)$	${}X^{2}+1$	${}X^{2}+1$	${}(X+5)(X+8)$
5	${}X^{4}+X^{3}+X^{2}+X+1$	${}X^{4}+X^{3}+X^{2}+X+1$	${}X^{4}+X^{3}+X^{2}+X+1$	${}(X+4)^{4}$	${}X^{4}+X^{3}+X^{2}+X+1$	${}(X+2)(X+6)(X+7)(X+8)$	${}X^{4}+X^{3}+X^{2}+X+1$
6	${}X^{2}-X+1$	${}X^{2}-X+1$	${}(X+1)^{2}$	${}X^{2}-X+1$	${}(X+2)(X+4)$	${}X^{2}-X+1$	${}(X+3)(X+9)$
7	${}X^{6}+X^{5}+X^{4}+X^{3}+X^{2}+X+1$	${}(X^{3}+X+1)(X^{3}+X^{2}+1)$	${}X^{6}+X^{5}+X^{4}+X^{3}+X^{2}+X+1$	${}X^{6}+X^{5}+X^{4}+X^{3}+X^{2}+X+1$	${}(X+6)^{6}$	${}(X^{3}+5X^{2}+4X+10)(X^{3}+7X^{2}+6X+10)$	${}(X^{2}+3X+1)(X^{2}+5X+1)(X^{2}+6X+1)$
8	${}X^{4}+1$	${}(X+1)^{4}$	${}(X^{2}+2X+2)(X^{2}+X+2)$	${}(X^{2}+3)(X^{2}+2)$	${}(X^{2}+4X+1)(X^{2}+3X+1)$	${}(X^{2}+8X+10)(X^{2}+3X+10)$	${}(X^{2}+8)(X^{2}+5)$
9	${}X^{6}+X^{3}+1$	${}X^{6}+X^{3}+1$	${}(X+2)^{6}$	${}X^{6}+X^{3}+1$	${}(X^{3}+5)(X^{3}+3)$	${}X^{6}+X^{3}+1$	${}(X^{3}+10)(X^{3}+4)$
10	${}X^{4}-X^{3}+X^{2}-X+1$	${}X^{4}-X^{3}+X^{2}-X+1$	${}X^{4}-X^{3}+X^{2}-X+1$	${}(X+1)^{4}$	${}X^{4}-X^{3}+X^{2}-X+1$	${}(X+9)(X+5)(X+4)(X+3)$	${}X^{4}-X^{3}+X^{2}-X+1$
12	${}X^{4}-X^{2}+1$	${}(X^{2}+X+1)^{2}$	${}(X^{2}+1)^{2}$	${}(X^{2}+2X+4)(X^{2}+3X+4)$	${}(X^{2}+4)(X^{2}+2)$	${}(X^{2}+6X+1)(X^{2}+5X+1)$	${}(X+11)(X+7)(X+6)(X+2)$
15	${}X^{8}-X^{7}+X^{5}-X^{4}+X^{3}-X+1$	${}(X^{4}+X+1)(X^{4}+X^{3}+1)$	${}(X^{4}+X^{3}+X^{2}+X+1)^{2}$	${}(X^{2}+X+1)^{4}$	${}(X^{4}+4X^{3}+2X^{2}+X+4)(X^{4}+2X^{3}+4X^{2}+X+2)$	${}(X^{2}+3X+9)(X^{2}+9X+4)(X^{2}+4X+5)(X^{2}+5X+3)$	${}(X^{4}+3X^{3}+9X^{2}+X+3)(X^{4}+9X^{3}+3X^{2}+X+9)$