What conditions are necessary on q for it to be a divisor of a^p+1 if p and q are both prime?

- Mar 16th 2009, 02:06 PMgummy_ratzProof
What conditions are necessary on q for it to be a divisor of a^p+1 if p and q are both prime?

- Mar 17th 2009, 12:57 PMThePerfectHacker
We notice that . We will also assume that are odd primes.

If . Let be the order of mod . This forces . If then and so , thus . If then . And so , however, this is an unintersting case because there is no restriction on . Thus, we can safely assume that . Thus, in either case since . Thus, we require that divides . - Mar 17th 2009, 08:49 PMgummy_ratz
Thanks!