Regular ternary sums of generalized polygonal numbers

TL;DR

This paper establishes a specific constant beyond which no regular ternary sum of generalized m-gonal numbers exists, advancing understanding of their distribution.

Contribution

It provides an explicit constant C, proving the non-existence of regular ternary sums of generalized m-gonal numbers for all m > C.

Findings

Identifies an explicit constant C for generalized m-gonal numbers.

Proves non-existence of regular ternary sums beyond this constant.

Enhances understanding of the structure of generalized polygonal numbers.

Abstract

In this article, we provide an explicit constant $C$ such that there is no regular ternary sum of generalized $m$-gonal numbers for any integer $m$ greater than $C$.