Generalization of a problem of Lehmer

Cristian Cobeli, Alexandru Zaharescu

Research output: Contribution to journalArticlepeer-review


Given a prime number p, Lehmer raised the problem of investigating the number of integers a ∈ {1, 2, . . . , p - 1} for which a and ā are of opposite parity, where ā ∈ {1, 2, . . . , p - 1} is such that a ā ≡ 1 (mod p). We replace the pair (a, ā) 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.

Original languageEnglish (US)
Pages (from-to)301-307
Number of pages7
JournalManuscripta Mathematica
Issue number3
StatePublished - Mar 2001

ASJC Scopus subject areas

  • General Mathematics


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