## Experimental Mathematics

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

Meinhard Peters

#### 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

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

#### 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