Quadratic Residues and the Quadratic Reciprocity Law

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


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
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.


Diophantine Equation Quadratic Residue Multiplicative Property Legendre Symbol Linear Congruence 


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Copyright information

© Springer Science+Business Media New York 1976

Authors and Affiliations

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

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