Experimental Mathematics

The Diophantine Equation $ xy + yz + xz = n $ and Indecomposable Binary Quadratic Forms

Meinhard Peters

Full-text: Open access

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.

Article information

Source
Experiment. Math. Volume 13, Issue 3 (2004), 273-274.

Dates
First available in Project Euclid: 22 December 2004

Permanent link to this document
https://projecteuclid.org/euclid.em/1103749835

Mathematical Reviews number (MathSciNet)
MR2103325

Zentralblatt MATH identifier
1147.11314

Subjects
Primary: 11E12: Quadratic forms over global rings and fields 11E96
Secondary: 11D09: Quadratic and bilinear equations

Keywords
Binary quadratic forms Diophantine equations

Citation

Peters, Meinhard. The Diophantine Equation $ xy + yz + xz = n $ and Indecomposable Binary Quadratic Forms. Experiment. Math. 13 (2004), no. 3, 273--274. https://projecteuclid.org/euclid.em/1103749835.


Export citation