On a property of superposition of the generating functions ln(1/(1-F(x)))

TL;DR

This paper introduces a new property of the superposition of generating functions, enabling the construction of primality tests based on compositions of positive numbers and their mathematical properties.

Contribution

It presents a novel property of the superposition of generating functions ln(1/(1-F(x))) and develops related theorems for primality testing.

Findings

New property of generating function superposition established

Theorems and corollaries for primality tests derived

Examples demonstrating the application of the property provided

Abstract

Obtained a new property of superposition of the generating functions ln(1/(1-F(x))), where F(x) - generating function with integer coefficients, which allows the construction a primality tests. The theorem which is based on compositions of positive numbers and its corollary are proved. Examples are given. Key words: Generating functions, superposition of generating functions, composition of a natural number.