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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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Publish Page: 
Furnished by JSTOR: 
File Content: 
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
Average: 3 (5 votes)

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