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arXiv · 1211.2100

Integer properties of a composition of exponential generating functions

Dmitry Kruchinin
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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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Dmitry Kruchinin. 2012-11-09. Integer properties of a composition of exponential generating functions. https://arxiv.org/abs/1211.2100

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