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On Positive Integer Solutions of the Equation xy + yz + xz = n

Published online by Cambridge University Press:  20 November 2018

Al-Zaid Hassan ,
B. Brindza  and
Á. Pintér
Al-Zaid Hassan
Affiliation:
Kuwait University, P.O.Box 5969, Safat 13060, Kuwait
B. Brindza
Affiliation:
Kuwait University, P.O.Box 5969, Safat 13060, Kuwait, e-mail: brindza@math-1.sci.kuniw.edu.kw
Á. Pintér
Affiliation:
Department of Mathematics, Kossuth University, P.O. Box 12, 4010 Debrecen, Hungary, E-mail: pinter@huklte51.bitnet
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Abstract

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As it had been recognized by Liouville, Hermite, Mordell and others, the number of non-negative integer solutions of the equation in the title is strongly related to the class number of quadratic forms with discriminant —n. The purpose of this note is to point out a deeper relation which makes it possible to derive a reasonable upper bound for the number of solutions.

Keywords

11D0911R29class numbersdiophantine equationsquadratic forms
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 39 , Issue 2 , 01 June 1996 , pp. 199 - 202
Copyright
Copyright © Canadian Mathematical Society 1996

References

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