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On Diophantine triples containing a triangular number

Marija Bliznac Trebješanin

Abstract

A general construction yielding infinitely many families of $D(m^2)$-triples of triangular numbers is presented. Moreover, each triple obtained from this construction contains the same triangular number $T_n$.

On Diophantine triples containing a triangular number

Abstract

A general construction yielding infinitely many families of -triples of triangular numbers is presented. Moreover, each triple obtained from this construction contains the same triangular number .

Paper Structure

This paper contains 2 sections, 1 theorem, 22 equations.

Table of Contents

  1. Introduction
  2. Constructing Diophantine triples

Key Result

Theorem 1

Let $m$ be a positive integer. For every positive integer $n$, triangular number $T_n$ is a member of infinitely many $D(m^2)$-triples of triangular numbers.

Theorems & Definitions (2)

  • Theorem 1
  • Remark