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ON THE NUMBER OF SOLUTIONS OF THE DIOPHANTINE EQUATION axm−byn=c

Part of: Diophantine equations

Published online by Cambridge University Press:  13 January 2010

BO HE  and
ALAIN TOGBÉ
BO HE
Affiliation:
Department of Mathematics, ABA Teachers College, Wenchuan, Sichuan 623000, PR China (email: bhe@live.cn)
ALAIN TOGBÉ*
Affiliation:
Mathematics Department, Purdue University North Central, 1401 South US 421, Westville IN 46391, USA (email: atogbe@pnc.edu, atogbe@juno.com)
*
✉For correspondence; e-mail: atogbe@jun.com
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Abstract

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Let a, b, c, x and y be positive integers. In this paper we sharpen a result of Le by showing that the Diophantine equation has at most two positive integer solutions (m,n) satisfying min (m,n)>1.

Keywords

exponential equationsDiophantine equations

MSC classification

Secondary: 11D61: Exponential equations

Information

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 81 , Issue 2 , April 2010 , pp. 177 - 185
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2010

Footnotes

The first author was supported by the Applied Basic Research Foundation of Sichuan Provincial Science and Technology Department (No. 2009JY0091). The second author is grateful to Purdue University North Central for the support.

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