manuscripta mathematica

, Volume 104, Issue 3, pp 301–307

Generalization of a problem of Lehmer

  • Cristian Cobeli
  • Alexandru Zaharescu

DOI: 10.1007/s002290170028

Cite this article as:
Cobeli, C. & Zaharescu, A. manuscripta math. (2001) 104: 301. doi:10.1007/s002290170028


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

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
  2. 2.Department of Mathematics, University of Illinois at Urbana-Champaign, Altgeld Hall, 1409 W. Green Street, Urbana, IL 61801, USA.¶e-mail: zaharesc@math.uiuc.eduUS