manuscripta mathematica

, Volume 104, Issue 3, pp 301–307 | Cite as

Generalization of a problem of Lehmer

  • Cristian Cobeli
  • Alexandru Zaharescu

Abstract:

Given a prime number p, Lehmer raised the problem of investigating the number of integers \(\) for which a and \(\) are of opposite parity, where \(\) is such that \(\). We replace the pair \(\) by a point lying on a more general irreducible curve defined mod p and instead of the parity conditions on the coordinates more general congruence conditions are considered. An asymptotic result is then obtained for the number of such points.

Mathematics Subject Classification (2000): 11T99 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Cristian Cobeli
    • 1
  • Alexandru Zaharescu
    • 1
  1. 1.Institute of Mathematics of the Romanian Academy,¶ P.O. Box 1-764, 70700 Bucharest, Romania. e-mail: ccobeli@stoilow.imar.roRO

Personalised recommendations