A fixed point of formula_20 is a zero of the function formula_21. In the ring of integers modulo formula_1, there are formula_23 zeroes to formula_24, where the prime omega function formula_25 is the number of distinct prime factors in formula_1. An element formula_27 in formula_28 is a zero of formula_24 if and only if formula_30 or formula_31 for all formula_32. Since there are two possible values in formula_33, and there are formula_25 such formula_32, there are formula_23 zeroes of formula_24, and thus there are formula_23 fixed points of formula_6. According to Hensel's lemma, if there are formula_4 zeroes or fixed points of a polynomial function modulo formula_1, then there are formula_4 corresponding zeroes or fixed points of the same function modulo any power of formula_1, and this remains true in the inverse limit. Thus, in any given base formula_1 there are formula_23 formula_1-adic fixed points of formula_6.