  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.).
