# Cantor series expansions of rational numbers

## TL;DR

This survey explores the conditions under which rational numbers can be represented using Cantor series, providing necessary and sufficient criteria for arbitrary sequences.

## Contribution

It offers a comprehensive set of necessary and sufficient conditions for representing rational numbers via Cantor series with any given sequence.

## Key findings

- Established necessary and sufficient conditions for rational representations
- Generalized conditions for arbitrary sequences $(q_k)$
- Enhanced understanding of Cantor series representations

## Abstract

This survey is devoted to necessary and suffcient conditions for a rational number to be representable by a Cantor series. Necessary and suffcient conditions are formulated for the case of an arbitrary sequence $(q_k)$.