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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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