On some problems of expansions investigated
by P. Erdős et al.

Abstract. The objective of this article is twofold: First, we review the key results achieved by P. Erdős and his co-authors in the field of non-integer based expansions. On the other hand, in many places we present possible generalizations, and colourful, interesting examples; with the purpose of drawing attention of hopeful new researchers to this very interesting area.

Key words and phrases. Generalized number systems, expansions of numbers, greedy and unique expansions.