MODELING OF THE PRIMITIVE ROOTS STRUCTURE THAT ARE ASSOCIATED WITH GIVEN PRIME NUMBERS

Abstract

The problem of calculating the set of all primitive roots of an arbitrary prime number is considered. The algorithm for checking the natural number on the property of being the primitive root of a given prime number is constructed. The properties of the structures of recursive cycles of primitive roots are investigated. It is proved that all primitive roots of any prime number form pairs in which the recursive cycle of one is the inverse of the recursive cycle of the other element of the pair. The possibilities of representing recursive cycles in two-dimensional space are investigated. It is shown that recursive cycles form dynamic processes.