Suppose that p is a prime number and g is primitive root. Prove that the least residues of 4 9²,9ª, 96, 98,..., 9º−1 gp-1 are all of the quadratic residues modulo p.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.3: Zeros Of Polynomials
Problem 56E
Question
Suppose that p is a prime number and g is primitive root. Prove that the least residues of
4
9²,9ª, 96, 98,..., 9º−1
gp-1
are all of the quadratic residues modulo p.
Transcribed Image Text:Suppose that p is a prime number and g is primitive root. Prove that the least residues of 4 9²,9ª, 96, 98,..., 9º−1 gp-1 are all of the quadratic residues modulo p.
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