Numeric Palindromes in Primitive and Non-primitive Pythagorean Triples

TL;DR

This paper investigates the occurrence of numeric palindromes within primitive and non-primitive Pythagorean triples, establishing the infinitude of such triples containing one, two, or three palindromic components and discussing related open problems.

Contribution

It proves the existence of infinitely many Pythagorean triples with one, two, or three palindromic components, including primitive triples, and presents open problems in this area.

Findings

Infinitely many non-primitive triples with palindromic components

Existence of primitive triples with palindromic components

Open problems related to palindromes in primitive triples

Abstract

In this article we consider numeric palindromes as a component of a pythagorean triple. We first show that there are infinitely many non-primitive pythagorean triples that contains (i) a single numeric palindrome as a component, (ii) two numeric palindromes as a component and (iii) three numeric palindromes as a component. We then focus on numeric palindromes in primitive pythagorean triples. Open problem related to the topic was also given.