2011/09/08 by Dmitry Kruchinin, Kruchinin, Dmitry, Yuriy Shablya +1
Mathematics · Physics and Astronomy · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Advanced Mathematical Theories and Applications #math.CO #math.NT
paper · pdf · doi:10.48550/arxiv.1109.1683
arxiv created 2015/06/19 · arxiv updated 2015/06/22
In this paper, we consider properties of coefficients of a generating functions composition, where the outer function is a logarithmic generating function and the inner function is an ordinary generating function with integer coefficients. Using notions of composita and composition of generating functions, we get new properties for this composition. The properties can be used for distinguishing prime numbers from composite numbers. As an application, obtained results can be used to obtain new primality criteria. We obtain primality criteria for the Mersenne numbers, the Lucas numbers, the Pell-Lucas numbers, the Jacobsthal-Lucas numbers, and the Lucas sequences. Keywords: generating function, composition of generating function, composita, primality criterion.