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On a problem of Diophantus for higher powers

Published online by Cambridge University Press:  26 June 2003

YANN BUGEAUD  and
ANDREJ DUJELLA
YANN BUGEAUD
Affiliation:
Université Louis Pasteur, U. F. R. de mathématiques, 7, rue René Descartes, 67084 Strasbourg, France. e-mail: [email protected]
ANDREJ DUJELLA
Affiliation:
University of Zagreb, Department of Mathematics, Bijenička cesta 30, 10000 Zagreb, Croatia. e-mail: [email protected]
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Abstract

Let $k\ge 3$ be an integer. We study the possible existence of finite sets of positive integers such that the product of any two of them increased by 1 is a $k$th power.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 135 , Issue 1 , July 2003 , pp. 1 - 10
Copyright
2003 Cambridge Philosophical Society

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