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Rational points on the superelliptic Erdös Selfridge curve of fifth degree

Part of: Diophantine equations

Published online by Cambridge University Press:  26 February 2010

M. Lakhal  and
J. W. Sander
M. Lakhal
Affiliation:
Institut für Mathematik, Universität Hannover, Welfengarten 1, 30167 Hannover, Germany.
J. W. Sander
Affiliation:
Institut für Mathematik, Universität Hannover, Welfengarten 1, 30167 Hannover, Germany.
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Extract

§1. Introduction, By a remarkable result of Erdos and Selfridge [3] in 1975. the diophantine equation

with integers k≥2 and m≥2, has only the trivial solutions. x = −j(j = i, …, m), y = 0. This put an end to the old question whether the product of consecutive positive integers could ever be a perfect power; for a brief account of its history see [7].

MSC classification

Secondary: 11D41: Higher degree equations; Fermat's equation

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Type
Research Article
Information
Mathematika , Volume 50 , Issue 1-2 , December 2003 , pp. 113 - 124
Copyright
Copyright © University College London 2003

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References

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