TY - JOUR

T1 - Generalization of a problem of Lehmer

AU - Cobeli, Cristian

AU - Zaharescu, Alexandru

PY - 2001/3

Y1 - 2001/3

N2 - 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.

AB - 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.

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U2 - 10.1007/s002290170028

DO - 10.1007/s002290170028

M3 - Article

AN - SCOPUS:0035532308

SN - 0025-2611

VL - 104

SP - 301

EP - 307

JO - Manuscripta Mathematica

JF - Manuscripta Mathematica

IS - 3

ER -