# The Quadratic Character of $2$

The number $2$ is a quadratic residue mod $p$ if $p = 8k + 1$ or $p = 8k + 7$, but not if $p = 8k + 3$ or $p = 8k + 5$. This is proved by a simple counting argument, assuming the existence of a primitive root mod $p$.

Old Node ID:
3869
MSC Codes:
11-XX
Author(s):
Rafael Jakimczuk (Universidad Nacional de Luján Argentina)
Publication Date:
Monday, April 9, 2012
Original Publication Source:
Mathematics Magazine
Original Publication Date:
April, 2011
Subject(s):
Algebra and Number Theory
Number Theory
Topic(s):
Congruences, Solving Congruence Equations
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Rating Count:
5.00
Rating Sum:
15.00
Rating Average:
3.00
Applicable Course(s):
4.3 Number Theory
Modify Date:
Saturday, August 25, 2012