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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Affine curves with infinitely many integral points


Author: Dimitrios Poulakis
Journal: Proc. Amer. Math. Soc. 131 (2003), 1357-1359
MSC (2000): Primary 11G30, 14G25, 11D41
Published electronically: October 1, 2002
MathSciNet review: 1949864
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Abstract: Let $C \subset {\mathbf{A}}^{n}$ be an irreducible affine curve of (geometric) genus 0 defined by a finite family of polynomials having integer coefficients. In this note we give a necessary and sufficient condition for $C$ to possess infinitely many integer points, correcting a statement of J. H. Silverman (Theoret. Comput. Sci., 2000).


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Additional Information

Dimitrios Poulakis
Affiliation: Department of Mathematics, Aristotle University of Thessaloniki, 54124 Thessaloniki, Greece
Email: poulakis@auth.gr

DOI: http://dx.doi.org/10.1090/S0002-9939-02-06841-7
PII: S 0002-9939(02)06841-7
Received by editor(s): March 19, 2001
Received by editor(s) in revised form: January 8, 2002
Published electronically: October 1, 2002
Communicated by: Michael Stillman
Article copyright: © Copyright 2002 American Mathematical Society