Hostname: page-component-78c5997874-ndw9j Total loading time: 0 Render date: 2024-11-15T10:38:57.170Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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