# Modeling rational numbers by Cantor series

## TL;DR

This paper explores how rational numbers can be modeled using Cantor series, establishing relations between their digits in these representations for arbitrary sequences.

## Contribution

It provides new proofs of relations between digits in Cantor series representations of rational numbers with arbitrary sequences.

## Key findings

- Relations between digits are established for rational numbers in Cantor series.
- Proofs are provided for arbitrary sequences $(q_k)$ in Cantor series.
- The paper enhances understanding of rational number representations via Cantor series.

## Abstract

In the present article, modeling certain rational numbers, that are represented in terms of Cantor series, are described. The statements on relations between digits in the representations of rational numbers by Cantor series (for the case of an arbitrary sequence $(q_k)$) are proved.