N-sociable Heronian Triangles

TL;DR

This paper introduces the concept of n-sociable Heronian triangles, generalizing amicable Heronian triangles, and provides characterizations for these for each n, expanding the understanding of integer-sided triangles with integer areas.

Contribution

It generalizes the concept of amicable Heronian triangles to n-sociable ones and characterizes their properties for any number n, advancing the study of special integer triangles.

Findings

Defined n-sociable Heronian triangles

Characterized n-sociable triangles for each n

Extended the concept of amicable Heronian triangles

Abstract

A Heronian triangle is a triangle that has integer side lengths and integer area. Praton and Shalqini [1] define amicable Heronian triangles to be two Heronian triangles where the area of one equals the perimeter of the other, and vice versa; analogous to the concept of amicable numbers. In this paper, we generalize this notion to n-sociable Heronian triangles and characterize them for each n.