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The order of inverses mod q

Part of: Multiplicative number theory

Published online by Cambridge University Press:  26 February 2010

Cristian Cobeli  and
Alexandru Zaharescu
Cristian Cobeli
Affiliation:
Institute of Mathematics of the Romanian Academy, P.O. Box 1-764, 70700 Bucharest, Romania.
Alexandru Zaharescu
Affiliation:
Institute of Mathematics of the Romanian Academy, P.O. Box 1-764, 70700 Bucharest, Romania.
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Abstract

Let q be a prime number and let a = (a1, …, as) be an s-tuple of distinct integers modulo q. For any x coprime with q, let be such that . For fixed s and q→∞ an asymptotic formula is given for the number of residue classes x modulo q for which

The more general case, when q is not necessarily prime and x is restricted to lie in a given subinterval of [1, q], is also treated.

MSC classification

Secondary: 11N69: Distribution of integers in special residue classes
Type
Research Article
Information
Mathematika , Volume 47 , Issue 1-2 , December 2000 , pp. 87 - 108
Copyright
Copyright © University College London 2000

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