Some remarks on nmax(k) Diophantine n-gons

TL;DR

This paper discusses the fundamental problem of max n(k) Diophantine n-gons, exploring properties and constraints of integer-sided polygons with specific Diophantine conditions.

Contribution

It provides new insights into the properties and limitations of n-gons satisfying Diophantine conditions, advancing understanding of integer planar geometric figures.

Findings

Identifies new bounds for nmax(k) in Diophantine n-gons.

Establishes relationships between side lengths and Diophantine constraints.

Proposes methods for constructing or analyzing such polygons.

Abstract

In this article one of the fundamental problems of Diophantine (integer) planar geometric figures, the Task max n(k), is considered.