Quadratic Residues

  • Lindsay N. Childs
Part of the Undergraduate Texts in Mathematics book series (UTM)


In this chapter we describe a procedure for deciding efficiently whether or not the number a is a square modulo m. The main result, known as the law of quadratic reciprocity, was first proved by Gauss (1801) and is a cornerstone of number theory. The last section gives some applications of quadratic reciprocity to primality testing and testing for primitive roots.


Primitive Element Primitive Root Chinese Remainder Theorem Quadratic Residue Congruence Class 
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 Science+Business Media New York 1995

Authors and Affiliations

  • Lindsay N. Childs
    • 1
  1. 1.Department of MathematicsSUNY at AlbanyAlbanyUSA

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