Narayana numbers as product of three repdigits in base $g$

TL;DR

This paper investigates Narayana numbers that can be expressed as the product of three repdigits in various bases, establishing finiteness and explicitly determining all such numbers for bases 2 through 10.

Contribution

It proves the finiteness of Narayana numbers as products of three repdigits and explicitly finds all such numbers for bases 2 to 10.

Findings

Finitely many Narayana numbers are products of three repdigits in base g.

Complete classification of these numbers for bases 2 to 10.

Method for identifying such numbers in different bases.

Abstract

In this paper, we show that there are only finitely many Narayana's numbers which can be written as product of three repdigits in base $g$ with $g \geq 2$. Moreover, for $2 \leq g \leq 10$, we determine all these numbers.