Question

Challenge:
Let p be a prime number and x be an integer. Then prove that every prime divisor q of 1 + x + . . + x^p−1 either satisfies q ≡ 1 (mod p) or q = p.

Answer 1

Cyclotomic Polynomials huh?

Answer 2

Yup.

Answer 3

http://www.yimin-ge.com/doc/cyclotomic_polynomials.pdf has the proof.

Answer 4

Can you provide one using complex numbers?