Experimental Mathematics

On certain plane curves with many integral points

Fernando Rodriguez Villegas and José Felipe Voloch

Abstract

We define a sequence of polynomials $P_d \in \funnyZ[x,y]$, such that $P_d$ is absolutely irreducible, of degree d, has low height, and has at least $d^2+2d+3$ 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.

Article information

Source
Experiment. Math., Volume 8, Issue 1 (1999), 57-62.

Dates
First available in Project Euclid: 12 March 2003

Permanent link to this document
https://projecteuclid.org/euclid.em/1047477112

Mathematical Reviews number (MathSciNet)
MR1685037

Zentralblatt MATH identifier
1029.11025

Subjects
Primary: 14G05: Rational points
Secondary: 11G30: Curves of arbitrary genus or genus = 1 over global fields [See also 14H25]

Citation

Rodriguez Villegas, Fernando; Voloch, José Felipe. On certain plane curves with many integral points. Experiment. Math. 8 (1999), no. 1, 57--62. https://projecteuclid.org/euclid.em/1047477112


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