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Suppose that p≥ 5 is prime. Show that -3 is a quadratic residue (mo p) if p = 1 or 7 (mod 12) and a nonresidue if p = 5 or 11 (mod 12).

Suppose that p≥ 5 is prime. Show that -3 is a quadratic residue (mo p) if p = 1 or 7 (mod 12) and a nonresidue if p = 5 or 11 (mod 12).

Elements Of Modern Algebra
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter2: The Integers
Section2.4: Prime Factors And Greatest Common Divisor
Problem 5E: Prove that if p and q are distinct primes, then there exist integers m and n such that pm+qn=1.
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(a) Suppose that p≥ 5 is prime. Show that -3 is a quadratic residue (mod p) if p = 1 or 7 (mod 12) and a nonresidue if p = 5 or 11 (mod 12).
Transcribed Image Text:(a) Suppose that p≥ 5 is prime. Show that -3 is a quadratic residue (mod p) if p = 1 or 7 (mod 12) and a nonresidue if p = 5 or 11 (mod 12).
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