About Some Relatives of the Taxicab Number

TL;DR

This paper explores generalizations of the unique properties of the taxicab number 1729, focusing on digit sums, reversals, and multiplicative relationships.

Contribution

It introduces new generalizations of the taxicab number property, extending the classical example to broader numerical contexts.

Findings

Identified new classes of numbers with similar digit-reversal and multiplication properties

Established conditions under which these properties hold for generalized numbers

Provided examples illustrating the extended properties

Abstract

The taxicab number, $1729$, has the following property. If we add its digits we obtain $19$. The number obtained from $19$ by reversing the order of its digits is $91$. If we multiply $19$ by $91$ we obtain again $1729$. In the paper we study various generalizations of this property.