The main results of this paper give two criteria for certain infinite series of rational numbers to be Liouville. Some examples are also included.Keywords: Liouville numbers, Infinite… Expand

Abstract The main results of this paper give several criteria for certain infinite series of rational numbers to be irrational, transcendental or Liouville. Criteria are based on specific reccurence… Expand

Following Erdős [1] we say a sequence {an}∞n=1 is irrational if the set { ∑ n≥1 1 ancn | cn ∈ N}, which we refer to henceforth as its expressible set, contains no rational numbers. In [1] it is shown… Expand

While the Science Olympiads have a long tradition, the new competition of the 21st century European Union Science Olympiad (EUSO) has not even reached ten years. Annually young people aged around 16… Expand