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On the equation \ x^y\pm y^x=\prod n_i!

Published online by Cambridge University Press:  08 November 2000

Florian Luca ,
Maurice Mignotte  and
Yves Roy
Florian Luca
Affiliation:
Department of Mathematics, Bielefeld University, 33 501 Bielefeld, Germany
Maurice Mignotte
Affiliation:
Department of Mathematics, University Louis Pasteur, 67 084 Strasbourg, France
Yves Roy
Affiliation:
Department of Mathematics, University Louis Pasteur, 67 084 Strasbourg, France
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Abstract

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In this note we investigate the diophantine equation<$$>x^y\pm y^x=\prod n_i!<$$>

where x and y are odd and greater than 1. We prove that this equation has no integer solutions.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 42 , Issue 3 , September 2000 , pp. 351 - 357
Copyright
1999 Glasgow Mathematical Journal Trust