This article is cited in 1 paper

Theoretical Foundations of Applied Discrete Mathematics

Properties of coefficients in some superpositions of generating functions

D. V. Kruchinin

Tomsk State University of Control Systems and Radioelectronics, Tomsk, Russia

Abstract: The generating function $ \ln((1-F(x))^{-1})$ where $F(x)$ is an ordinary generating function with the integer coefficients is considered. Some properties ot its coefficients allowing the construction of probabilistic primality tests are obtained. The connection of them with the existing primality tests is shown. Some new properties of Lucas numbers and binomial coefficients $2n-1\choose n-1$ are obtained too.

Keywords: generating functions, superposition of generating functions, composition of a natural number, primality test.

UDC: 511+519.1