Let a be a quadratic residue of the odd prime p. (1) Prove that a is not a primitive root modulo p (2) Prove that p−a is a quadratic residue or nonresidue of p according as p≡1( mod 4) orp≡3(mod 4)

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter6: More On Rings
Section6.3: The Characteristic Of A Ring
Problem 13E
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Let a be a quadratic residue of the odd prime p. (1) Prove that a is not a primitive root modulo p

(2) Prove that p−a is a quadratic residue or nonresidue of p according as p≡1( mod 4) orp≡3(mod 4)

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