Quadratic Residues and the Quadratic Reciprocity Law

  • Tom M. Apostol
Part of the Undergraduate Texts in Mathematics book series (UTM)

Abstract

As shown in Chapter 5, the problem of solving a polynomial congruence
can be reduced to polynomial congruences with prime moduli plus a set of linear congruences. This chapter is concerned with quadratic congruences of the form
(1)
where p is an odd prime and (mod p). Since the modulus is prime we know that (1) has at most two solutions. Moreover, if x is a solution so is − x, hence the number of solutions is either 0 or 2.

Keywords

Diophantine Equation Quadratic Residue Multiplicative Property Legendre Symbol Linear Congruence 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer Science+Business Media New York 1976

Authors and Affiliations

  • Tom M. Apostol
    • 1
  1. 1.Department of MathematicsCalifornia Institute of TechnologyPasadenaUSA

Personalised recommendations