Integer properties of a composition of exponential generating functions

2012/11/09 by Dmitry Kruchinin, Kruchinin, Dmitry
Mathematics · #FOS: Mathematics #Number Theory (math.NT) #math.NT

paper · pdf · doi:10.48550/arxiv.1211.2100

8 pages

arxiv created 2012/11/09 · arxiv updated 2012/11/12

Abstract

In this paper, we study a composition of exponential generating functions. We obtain new properties of this composition, which allow to distinguish prime numbers from composite numbers. Using the result of paper we get the known properties of the Bell numbers(Touchard's Congruence for k=0) and new properties of the Euler numbers. Key words: exponential generating function, composition of generating functions, composita, primality, Touchard's Congruence, Bell numbers, Euler numbers.

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