# Repdigits as sums of three Padovan numbers

## TL;DR

This paper classifies all base-10 repdigits that can be expressed as the sum of three Padovan numbers, providing a complete characterization of such representations.

## Contribution

It determines all repdigits in base 10 that are sums of three Padovan numbers, a novel classification in the study of Padovan number representations.

## Key findings

- Identifies all repdigits as sums of three Padovan numbers
- Provides a complete list of such repdigits
- Advances understanding of Padovan number representations

## Abstract

Let $ \{P_{n}\}_{n\geq 0} $ be the sequence of Padovan numbers defined by $ P_0=0 $, $ P_1 =1=P_2$ and $ P_{n+3}= P_{n+1} +P_n$ for all $ n\geq 0 $. In this paper, we find all repdigits in base $ 10 $ which can be written as a sum of three Padovan numbers.