Diophantine Equations of Matching Games I

TL;DR

This paper investigates quadratic Diophantine equations linked to a specific class of matching games, highlighting the unique complexity and significance of the ternary case within this family.

Contribution

It introduces a new connection between Diophantine equations and matching games, focusing on the detailed analysis of the ternary case.

Findings

The ternary case is the most interesting and least arbitrary in the family.

Solutions to the quadratic Diophantine equations are characterized for the ternary case.

The study provides insights into the structure and properties of these equations.

Abstract

We solve a family of quadratic Diophantine equations associated to a simple kind of games. We show that the ternary case, in many ways, is the most interesting and the least arbitrary member of the family.