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In this topic we start with a general quadratic congruence equation modulo a given prime and we show, step-by-step, how to proceed. The first step is to simplify, using a substitution, to obtain a quadratic congruence in so called standard form. The idea now is to first determine if the quadratic congruence is solvable by doing computations using the Legendre symbol and the Law of Quadratic Reciprocity, and then to solve using brute force or more advanced techniques.

 

Books: number theory

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Elementary Number Theory  Elementary Number Theory
Authors: Gareth A. Jones, Josephine M. Jones

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Rating: 4.5 out of 5 stars 15 reviews
Sales Rank: 97693
Category: Book
ASIN: 3540761977
Publication Date: January 14, 1998
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An Introduction to the Theory of Numbers  An Introduction to the Theory of Numbers
Authors: G. H. Hardy, Edward M. Wright, Andrew Wiles

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Rating: 4.5 out of 5 stars 13 reviews
Sales Rank: 53801
Category: Book
ASIN: 0199219869
Publication Date: September 15, 2008
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Elementary Number Theory (6th Edition)  Elementary Number Theory (6th Edition)
Author: Kenneth H. Rosen

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Rating: 4.0 out of 5 stars 10 reviews
Sales Rank: 1381701
Category: Book
ASIN: 0321500318
Publication Date: April 5, 2010  (In 20 Days)
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Number Theory (Dover Books on Advanced Mathematics)  Number Theory (Dover Books on Advanced Mathematics)
Author: George E. Andrews

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Rating: 4.5 out of 5 stars 8 reviews
Sales Rank: 23774
Category: Book
ASIN: 0486682528
Publication Date: October 12, 1994
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Elementary Number Theory: Second Edition  Elementary Number Theory: Second Edition
Author: Underwood Dudley

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Rating: 5.0 out of 5 stars 5 reviews
Sales Rank: 73671
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ASIN: 048646931X
Publication Date: September 25, 2008
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Elementary Number Theory, 6th Edition  Elementary Number Theory, 6th Edition
Author: David M. Burton

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ASIN: 0070616078
Publication Date: September 27, 2005
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An Introduction to Number Theory (Graduate Texts in Mathematics)  An Introduction to Number Theory (Graduate Texts in Mathematics)
Authors: G. Everest, Thomas Ward

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ASIN: 1852339179
Publication Date: May 6, 2005
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Number Theory and Its History (Dover Classics of Science and Mathematics)  Number Theory and Its History (Dover Classics of Science and Mathematics)
Author: Oystein Ore

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Rating: 4.5 out of 5 stars 5 reviews
Sales Rank: 98858
Category: Book
ASIN: 0486656209
Publication Date: April 1, 1988
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Friendly Introduction to Number Theory, A (3rd Edition)  Friendly Introduction to Number Theory, A (3rd Edition)
Author: Joseph H. Silverman

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ASIN: 0131861379
Publication Date: March 31, 2005
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1001 Problems in Classical Number Theory  1001 Problems in Classical Number Theory
Author: Jean-Marie De Koninck and Armel Mercier

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ASIN: 0821842242
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