Quadratic Residues

  • Gareth A. Jones
  • J. Mary Jones
Part of the Springer Undergraduate Mathematics Series book series (SUMS)


In this chapter, we will consider the general question of whether an integer a has a square root mod (n), and if so, how many there are and how one can find them. One of the main applications of this is to the solution of quadratic congruences, but we will also deduce a proof that there are infinitely many primes p = 1 mod (4), and we will give a useful primality test for Fermat numbers.


Integer Point Primitive Root Chinese Remainder Theorem Quadratic Residue Fermat Number 
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Copyright information

© Springer-Verlag London 1998

Authors and Affiliations

  • Gareth A. Jones
    • 1
  • J. Mary Jones
    • 2
  1. 1.School of MathematicsUniversity of SouthamptonHighfieldUK
  2. 2.The Open UniversityWalton HallUK

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