Letgbe a primative root ofm. Anindexof a numberato the baseg(written $\displaystyle ind_{g}a$) is a numbertsuch that $\displaystyle g^{t} \equiv a \ (mod\ m)$. Given that $\displaystyle a \equiv b\ (mod\ m)$ and thatgis a primative root modulom, prove the following assertions:

i. $\displaystyle ind_{g}ac \equiv ind_{g}a + ind_{g}c\ \{mod\ \phi(m) \}$

ii. $\displaystyle ind_{g}a^{n} \equiv n\ ind_{g}a\ \{mod\ \phi(m) \}$

My problem mainly is that I don't fully understand primative roots.

Thanks!