4. Let p be a prime number and suppose that p = 3 (mod 4). Let A be any integer. Prove that exactly one of the following congruences, x²= A (mod p), = X2 A (mod p) has a solution.
4. Let p be a prime number and suppose that p = 3 (mod 4). Let A be any integer. Prove that exactly one of the following congruences, x²= A (mod p), = X2 A (mod p) has a solution.
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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