Cantor series and rational numbers

TL;DR

This paper investigates the conditions under which rational numbers can be represented by Cantor series, providing necessary and sufficient criteria for such representations in the context of arbitrary sequences.

Contribution

It formulates the necessary and sufficient conditions for representing rational numbers via positive Cantor series for any given sequence $(q_k)$.

Findings

Established criteria for rational number representation by Cantor series

Derived corollaries related to the representation conditions

Presented results at an international algebra conference

Abstract

The article is devoted to the investigation of representation of rational numbers by Cantor series. Necessary and sufficient conditions for a rational number to be representable by a positive Cantor series are formulated for the case of an arbitrary sequence $(q_k)$ and some its corollaries are considered. Results of this article were presented by the author of this article on the International Conference on Algebra dedicated to 100th anniversary of S. M. Chernikov (www.researchgate.net/publication/311415815, www.researchgate.net/publication/301849984). This investigation was also presented in some reports (links to the reports: www.researchgate.net/publication/303736670, www.researchgate.net/publication/303720573, etc.).