Counting Solutions of Congruences

  • Paul J. McCarthy
Part of the Universitext book series (UTX)


In this chapter we shall use the results obtained in the preceding chapter to count solutions of certain linear and other congruences in s unknowns. By a solution of a congruence, with modulus r, we mean a solution (mod r), i.e., an ordered s-tuple of integers (x1,…, xs) that satisfies the congruence, with two s-tuples (x1,…, xs) and \( \langle x_1^{'},...,x_s^{'}\rangle \) that satisfy the congruence counted as the same solution if and only if xi ≡ x1′. (mod r) for i = 1,…, s.


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Copyright information

© Springer-Verlag New York Inc. 1986

Authors and Affiliations

  • Paul J. McCarthy
    • 1
  1. 1.Department of MathematicsUniversity of KansasLawrenceUSA

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