# Extension of a Diophantine triple with the property $D(4)$

## TL;DR

This paper establishes an upper bound on how many ways a Diophantine triple with property D(4) can be extended to a quadruple and confirms the uniqueness of such an extension in specific cases.

## Contribution

It provides new bounds on extensions of Diophantine triples with property D(4) and verifies the conjecture of uniqueness in certain instances.

## Key findings

- Upper bound on the number of quadruple extensions
- Confirmation of the uniqueness conjecture in special cases
- Advancement in understanding Diophantine m-tuples with property D(4)

## Abstract

In this paper, we give an upper bound on the number of extensions of a triple to a quadruple for the Diophantine $m$-tuples with the property $D(4)$. We also confirm the conjecture of the uniqueness of such an extension in some special cases.