# Math Help - Elementary # theory

1. ## Elementary # theory

Hey, could anyone help me establish the following statements:

If a has order 2k modulo the odd prime p, then a^k= -1(mod p)

2. Originally Posted by felixmcgrady
Hey, could anyone help me establish the following statements:

If a has order 2k modulo the odd prime p, then a^k= -1(mod p)
Saying "a has order 2k modulo p" means that a^(2k)= 1 (mod p). Since p is a prime, either a^k= 1 or a^k= -1. If a^k= 1, then a has order k modulo p, not 2k.