On Narayana numbers which are products of four $b$-repdigits with a consequence

TL;DR

This paper investigates Narayana numbers that are expressible as products of four repdigits in various bases, establishing finiteness and complete classification for bases between 2 and 12.

Contribution

It proves finiteness and explicitly determines all such Narayana numbers for bases from 2 to 12.

Findings

Finitely many Narayana numbers are products of four repdigits for bases 2 to 12.

Complete classification of these numbers is achieved for each base.

The results extend understanding of special number representations in combinatorial number theory.

Abstract

In this paper, we focus on Narayana numbers which can be written as a products of four repdigits in base $g$, where $g$ is an integer with $g\geq2$. We prove that for $g$ between $2$ and $12$, there are finitely many of these numbers. Moreover we have fully determined them.