Nagell’s totient revisited

Pentti Haukkanen and R. Sivaramakrishnan
Notes on Number Theory and Discrete Mathematics, ISSN 1310–5132
Volume 4, 1998, Number 3, Pages 93–100
Full paper (PDF, 320 Kb)

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Authors and affiliations

Pentti Haukkanen
Department of Mathematical Sciences, University of Tampere,
P.O.Box 607, FIN-33101 Tampere, Finland

R. Sivaramakrishnan
Department of Studies in Mathematics, Mangalore University,
Dk 574199, India

Abstract

Nagell’s totient θ(n, r) counts the number of solutions of the congruence (*) n = x + y (mod r ) under the restriction (x, r) = (y, r) = 1. In this paper we evaluate the number θ(n, r, q) of solutions of the congruence (*) under the restriction (x,r) = (y,r) = q, where q|r, via Ramanathan’s approach to class-division of integers (mod r).

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