The main result of this paper is a criterion for linearly unrelated sequences which do not tend to infinity very fast. This criterion depends on divisibility. Applications and several examples are included. A problem of Erdös concerning the irrational sequences is partially solved.

No abstract

Abstract. The paper deals with a criterion for the sum of a special series to be a transcendental number. The result does not make use of divisibility properties or any kind of equation and depends only on the random oscillation of convergence.2000 Mathematics Subject Classification. 11J81.

The paper deals with lower estimates for the irrationality measure of the sum of a special series. The result depends only on the form of convergence and does not make use of divisibility properties of integers or any algebraic identities.