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SOME OBSERVATIONS ON THE DIOPHANTINE EQUATION y2=x!+A AND RELATED RESULTS

Part of: Diophantine equations

Published online by Cambridge University Press:  02 August 2012

MACIEJ ULAS
MACIEJ ULAS*
Affiliation:
Jagiellonian University, Faculty of Mathematics and Computer Science, Institute of Mathematics, Łojasiewicza 6, 30-348 Kraków, Poland (email: maciej.ulas@uj.edu.pl)
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Abstract

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We consider the Brocard–Ramanujan type Diophantine equation y2=x!+A and ask about values of A∈ℤ for which there are at least three solutions in the positive integers. In particular, we prove that the set 𝒜 consisting of integers with this property is infinite. In fact we construct a two-parameter family of integers contained in 𝒜. We also give some computational results related to this equation.

Keywords

factorial functionBrocard–Ramanujan type equationDiophantine equation

MSC classification

Secondary: 11D85: Representation problems
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 86 , Issue 3 , December 2012 , pp. 377 - 388
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2012

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