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1999 On certain plane curves with many integral points
Fernando Rodriguez Villegas, José Felipe Voloch
Experiment. Math. 8(1): 57-62 (1999).

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.

Citation

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Fernando Rodriguez Villegas. José Felipe Voloch. "On certain plane curves with many integral points." Experiment. Math. 8 (1) 57 - 62, 1999.

Information

Published: 1999
First available in Project Euclid: 12 March 2003

zbMATH: 1029.11025
MathSciNet: MR1685037

Subjects:
Primary: 14G05
Secondary: 11G30

Rights: Copyright © 1999 A K Peters, Ltd.

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Vol.8 • No. 1 • 1999
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