It's called theorem 8.9 in Rosen, Elementary Number Theory and it's Applications :P
It seems to be called the primitive root theorem
Suppose is prime and is a positive integer with . Then if is a primitive root modulo and modulo , then is a primitive root modulo for all positive integers . I am sure I have seen this somewhere, but I can't for the life of me remember where. If I can't find it (and no one here knows its name), I will try to prove it (or disprove it if I am remembering it incorrectly).