Experimental Mathematics
- Experiment. Math.
- Volume 13, Issue 3 (2004), 273-274.
The Diophantine Equation $ xy + yz + xz = n $ and Indecomposable Binary Quadratic Forms
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
