TITLE:
Average Probability of an Element Being a Generator in the Cyclic Group
AUTHORS:
Yoshihiro Tanaka
KEYWORDS:
Generator, Cyclic Group, Euler Product
JOURNAL NAME:
American Journal of Computational Mathematics,
Vol.13 No.2,
June
8,
2023
ABSTRACT: All
elements in the cyclic group are generated
by a generator g. The
number of generators ofof, namely is known to
be Euler’s totient function ; however, the average probability of an element
being a generator has not been discussed before. Several
analytic properties of have been investigated for a long time.
However, it seems that some issues still remain unresolved. In this
study, we derive the average probability of an element being a generator using previous classical studies.