Using the Law of Quadratic Reciprocity, prove that for an odd prime p ≠ 3 (3/p) = { 1 if p congruent to +- 1 (mod12); -1 if p congruent to +-5 (mod 12)
Using the Law of Quadratic Reciprocity, prove that for an odd prime p ≠ 3 (3/p) = { 1 if p congruent to +- 1 (mod12); -1 if p congruent to +-5 (mod 12)
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.5: The Binomial Theorem
Problem 16E
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Using the Law of Quadratic Reciprocity, prove that for an odd prime p ≠ 3
(3/p) = { 1 if p congruent to +- 1 (mod12); -1 if p congruent to +-5 (mod 12)
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