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A Diophantine Equation Associated to X0(5)

Published online by Cambridge University Press:  01 February 2010

Imin Chen
Imin Chen
Affiliation:
Department of Mathematics, Simon Fraser University, Burnaby, BC V5A 1S6, Canada, ichen@math.sfu.ca, http://www.math.sfu.ca/~ichen/

Abstract

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Several classes of Fermat-type diophantine equations have been successfully resolved using the method of galois representations and modularity. In each case, it is possible to view the proper solutions to the diophantine equation in question as corresponding to suitably defined integral points on a modular curve of level divisible by 2 or 3. Motivated by this point of view, an example of a diophantine equation associated to the modular curve X0(5) is discussed in this paper. The diophantine equation has four terms rather than the usual three terms characteristic of generalized Fermat equations.

Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 8 , 2005 , pp. 116 - 121
Copyright
Copyright © London Mathematical Society 2005

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