# Primative roots and indexes

Let g be a primative root of m. An index of a number a to the base g (written $ind_{g}a$) is a number t such that $g^{t} \equiv a \ (mod\ m)$. Given that $a \equiv b\ (mod\ m)$ and that g is a primative root modulo m, prove the following assertions:
i. $ind_{g}ac \equiv ind_{g}a + ind_{g}c\ \{mod\ \phi(m) \}$
ii. $ind_{g}a^{n} \equiv n\ ind_{g}a\ \{mod\ \phi(m) \}$