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THE EXPONENTIAL DIOPHANTINE EQUATION nx + (n + 1)y = (n + 2)z REVISITED

Published online by Cambridge University Press:  01 September 2009

BO HE  and
ALAIN TOGBÉ
BO HE
Affiliation:
College of Mathematics and Software Science, Sichuan Normal University, Chengdu 610068, People's Republic of China e-mail: bhe@live.cn
ALAIN TOGBÉ
Affiliation:
Mathematics Department, Purdue University North Central, 1401 S, U.S. 421, Westville, IN 46391, USA e-mail: atogbe@pnc.edu
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Abstract

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Let n be a positive integer. In this paper, we consider the diophantine equation We prove that this equation has only the positive integer solutions (n, x, y, z) = (1, t, 1, 1), (1, t, 3, 2), (3, 2, 2, 2). Therefore we extend the work done by Leszczyński (Wiadom. Mat., vol. 3, 1959, pp. 37–39) and Makowski (Wiadom. Mat., vol. 9, 1967, pp. 221–224).

Keywords

Primary 11D61secondary 11B3911J86
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 51 , Issue 3 , September 2009 , pp. 659 - 667
Copyright
Copyright © Glasgow Mathematical Journal Trust 2009

References

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