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Published in:
1986 | OriginalPaper | Chapter
Counting Solutions of Congruences
Author : Paul J. McCarthy
Published in: Introduction to Arithmetical Functions
Publisher: Springer New York
Included in: Professional Book Archive
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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.