Let p be an odd prime. Prove that (a) If p = 1 (mod 5) or p = 4 (mod 5), then 5 is quadratic residue of p. (b) If p = 2 (mod 5) or p = 3 (mod 5), then 5 is quadratic nonresidue of p.
Let p be an odd prime. Prove that (a) If p = 1 (mod 5) or p = 4 (mod 5), then 5 is quadratic residue of p. (b) If p = 2 (mod 5) or p = 3 (mod 5), then 5 is quadratic nonresidue of p.
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 33E: Use the fact that 3 is a prime to prove that there do not exist nonzero integers a and b such that...
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![Let p be an odd prime. Prove that
(a) If p = 1 (mod 5) or p = 4 (mod 5), then 5 is quadratic residue of p.
(b) If p = 2 (mod 5) or p = 3 (mod 5), then 5 is quadratic nonresidue of p.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F37ae482e-577b-435e-87c2-3546c2b78d91%2Ff048a0f8-29e1-432a-8b61-f49ae723da4d%2Fd90vmda_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Let p be an odd prime. Prove that
(a) If p = 1 (mod 5) or p = 4 (mod 5), then 5 is quadratic residue of p.
(b) If p = 2 (mod 5) or p = 3 (mod 5), then 5 is quadratic nonresidue of p.
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