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Math 110 Homework 4 Solutions - University of Michigan
www.math.lsa.umich.edu2 is a square root of 1 modulo p, as ( (p 1) 2)2 (p 1) 1 (mod p) by Fermat’s Little Theorem: But we proved in class that the only square roots of 1 modulo a prime are 1 and 1. Moreover, since is a primitive root, Part 1 of the theorem in Question 2 implies that (p 1) 2 cannot be congruent to 1, so we must have (p 1) 2 1 (mod p). It follows ...