Hello,

Can someone help me solve this problem with cyclotomic polynomials? is the n-th cyclotomic polynomial.

1. Let be a non-zero integer, a prime, a positive integer and . Prove that if and only if has period in .

2. Again assume . Prove that for some if and only if

Here's the source of the problem:

Algebra - Google Livres

Page 324, problem 21.

Thanks a lot.