As 0 is always a zero divisor, 0 and 1 are always fixed points of formula_6, and 0 and 1 are automorphic numbers in every base. These solutions are called trivial automorphic numbers. If formula_1 is a prime power, then the ring of formula_1-adic numbers has no zero divisors other than 0, so the only fixed points of formula_6 are 0 and 1. As a result, nontrivial automorphic numbers, those other than 0 and 1, only exist when the base formula_1 has at least two distinct prime factors.