ScholarLens Back to search
1996•Canadian Mathematical BulletinOpen access

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

Hassan Al-Zaid, Β. Brindza, Ákos Pintér

Open full text 5 citations

Abstract

Abstract 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.

Open-access reader

About this research paper

What this paper is about

Abstract 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.

Why it matters

OpenAlex reports 5 citations for this work. Citation counts describe recorded attention and do not establish research quality.

Key contribution

A contribution statement is not available in the OpenAlex record.

Method / approach

Method details are not available in the OpenAlex metadata.

Main findings

Findings are not separately available in the OpenAlex metadata.

Limitations

Limitations are not available in the OpenAlex metadata.

Applications

Application details are not available in the OpenAlex metadata.

Available abstract

Abstract 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.

Key concepts: Mathematics, Integer (computer science), Discriminant, Class number, Quadratic equation, Class (philosophy), Hermite polynomials, Combinatorics

Related papers

Related paper 1Related paper 2Related paper 3
Back to paper searchBrowse research topicsOriginal source
On Positive Integer Solutions of the Equation xy + yz + xz = n — Research Paper | ScholarLens