## Experimental Mathematics

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

### 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