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Generalization of a problem of Lehmer

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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.

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Authors and Affiliations

  1. Institute of Mathematics of the Romanian Academy,¶ P.O. Box 1-764, 70700 Bucharest, Romania. e-mail: ccobeli@stoilow.imar.ro, , , , , , RO

    Cristian Cobeli & Alexandru Zaharescu

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  1. Cristian Cobeli
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  2. Alexandru Zaharescu
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Received: 12 July 2000 / Revised version: 7 November 2000

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Cobeli, C., Zaharescu, A. Generalization of a problem of Lehmer. manuscripta math. 104, 301–307 (2001). https://doi.org/10.1007/s002290170028

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  • DOI: https://doi.org/10.1007/s002290170028

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