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Introduction: Solving the General Quadratic Congruence Modulo a Prime

  • Steve Wright
Chapter
Part of the Lecture Notes in Mathematics book series (LNM, volume 2171)

Abstract

The purpose of this chapter is to define quadratic residues and non-residues and to use the solution of the general quadratic congruence modulo a prime to indicate one reason why the study of quadratic residues and non-residues is interesting and important. This is done in Sect. 1.1. The primary source for essential information about quadratic residues is the Disquisitiones Arithmeticae of Carl Friedrich Gauss, one of the most important books about number theory ever written. Because of its singular prominence for number theory and also for what we will do in these lecture notes, the contents of the Disquisitiones are discussed briefly in Sect. 1.2, and some biographical facts about Gauss are also presented. Notation and terminology that will be employed throughout the sequel are recorded in Sect. 1.3, as well as a few basic facts from elementary number theory that will be used frequently in subsequent work.

Keywords

Quadratic Form Diophantine Equation Great Common Divisor Primitive Root Chinese Remainder Theorem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Steve Wright
    • 1
  1. 1.Department of Mathematics and StatisticsOakland UniversityRochesterUSA

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