let a, k, n be Nat; :: thesis: ( k is odd implies (a |^ n) + 1 divides (a |^ (n * k)) + 1 )
assume k is odd ; :: thesis: (a |^ n) + 1 divides (a |^ (n * k)) + 1
then consider b being Nat such that
A1: k = (2 * b) + 1 by ABIAN:9;
(a |^ n) + 1 divides ((a |^ n) |^ ((2 * b) + 1)) + (1 |^ ((2 * b) + 1)) by NEWTON01:35;
hence (a |^ n) + 1 divides (a |^ (n * k)) + 1 by A1, NEWTON:9; :: thesis: verum