Show that a is a generator for p if and only if ap-1qi mod

Question

Square and multiply:

Find 41105 mod 92.

Generators:-

Let p be prime and suppose that you know the factors of p - 1. Namely, p - 1 = q₁q₂ ··· q_n where each qi is prime. Show that a is a generator for p if and only if a(p-1)/qi mod p ≠ 1 for all i = 1, 2, ... , n. Use this test to determine if 3 is a generator for p = 11.