Use the fact that integers coprime to have multiplicative inverses mod Quick description ( Several results in elementary number theory are very easy consequences of the fact that the set of integers mod that are coprime to form a group under multiplication. )

Use the fact that the multiplicative group mod is cyclic Quick description ( Many results about arithmetic modulo a prime that might seem hard follow naturally and easily from the (non-obvious) fact that the group of non-zero integers mod under multiplication is cyclic. )