H Let a be a quadratic residue of the odd prime p.(a) Show that a is not a primitive root modulo p.(b) Show that p – a is a quadratic residue or nonresidue of p according as p = 1 (mod 4) or p = 3 (mod 4).

An integer a is referred to as quadratic residue modulo p if there exists n∈ℤ such that n2≡amod p.…

Answered: Let a be a quadratic residue of the odd…

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 51E: In the congruences ax b (mod n) in Exercises 40-53, a and n may not be relatively prime. Use the...

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Let a be a quadratic residue of the odd prime p. (a) Show that a is not a primitive root modulo p. (b) Show that p – a is a quadratic residue or nonresidue of p according as p=1 (mod 4) or p = 3 (mod 4)