Let p be an odd prime and a, b E Z such that (a, p) 1 and (b, p) = 1. Prove that if neither x² = a (mod p) nor x² = b (mod p) has solutions, then x² = ab (mod p) has solutions.
Let p be an odd prime and a, b E Z such that (a, p) 1 and (b, p) = 1. Prove that if neither x² = a (mod p) nor x² = b (mod p) has solutions, then x² = ab (mod p) has solutions.
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter2: The Integers
Section2.5: Congruence Of Integers
Problem 37E
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