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.
UR - http://www.scopus.com/inward/record.url?scp=0035532308&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0035532308&partnerID=8YFLogxK
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 -