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SOLUTIONS OF THE DIOPHANTINE EQUATION xy+yz+zx=n!

Published online by Cambridge University Press:  01 May 2008

MIHAI CIPU (BUCHAREST) ,
FLORIAN LUCA (MORELIA)  and
MAURICE MIGNOTTE (STRASBOURG)
MIHAI CIPU (BUCHAREST)
Affiliation:
Institute of Mathematics, Romanian Academy, P.O. Box 1–764, RO–014700 Bucharest, Romania and Université Louis Pasteur, Mathématique, 7, rue René Descartes, 67084 Strasbourg, France e-mail: mihai.cipu@imar.ro
FLORIAN LUCA (MORELIA)
Affiliation:
Instituto de Matemáticas, Universidad Autónoma de México, C.P. 58089, Morelia, Michoácan, México e-mail: fluca@matmor.unam.mx
MAURICE MIGNOTTE (STRASBOURG)
Affiliation:
Université Louis Pasteur, Mathématique, 7, rue René Descartes, 67084 Strasbourg, France e-mail: mignotte@math.u-strasbg.fr
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Abstract

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We prove that the only solutions in coprime positive integers to the equation are (x, y, z)=(n!–2, 1, 1, n), n≥3.

Keywords

11D6111D72
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 50 , Issue 2 , May 2008 , pp. 217 - 232
Copyright
Copyright © Glasgow Mathematical Journal Trust 2008

References

REFERENCES

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