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2004 The Diophantine Equation $ xy + yz + xz = n $ and Indecomposable Binary Quadratic Forms
Meinhard Peters
Experiment. Math. 13(3): 273-274 (2004).

Abstract

There are 18 (and possibly 19) integers that are not of the form $ xy + yz + xz $ with positive integers $x, y, z$. The same 18 integers appear as exceptional discriminants for which no indecomposable positive definite binary quadratic form exists. We show that the two problems are equivalent.

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Meinhard Peters. "The Diophantine Equation $ xy + yz + xz = n $ and Indecomposable Binary Quadratic Forms." Experiment. Math. 13 (3) 273 - 274, 2004.

Information

Published: 2004
First available in Project Euclid: 22 December 2004

zbMATH: 1147.11314
MathSciNet: MR2103325

Subjects:
Primary: 11E12 , 11E96
Secondary: 11D09

Keywords: binary quadratic forms , Diophantine equations

Rights: Copyright © 2004 A K Peters, Ltd.

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Vol.13 • No. 3 • 2004
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