Authors
Citation
Fr. Villegas et Jf. Voloch, On certain plane curves with many integral points, EXP MATH, 8(1), 1999, pp. 57-62
Citations number
6
Categorie Soggetti
Mathematics
Journal title
EXPERIMENTAL MATHEMATICS
ISSN journal
10586458
→ ACNP
Volume
8
Issue
1
Year of publication
1999
Pages
57 - 62
Database
ISI
SICI code
1058-6458(1999)8:1<57:OCPCWM>2.0.ZU;2-O
Abstract
We define a sequence of polynomials P-d is an element of Z [x, Y], such tha
t P-d is absolutely irreducible, of degree d, has low height, and has at le
ast d(2) + 2d + 3 integral solutions to P-d(x, y) = 0. We know of no other
nontrivial family of polynomials of increasing degree with as many integral
solutions in terms of their degree.