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Dirichlet, G.L. (1849) über die Bestimmung der mittleren Werthe in der Zahlentheorie. Verlag nicht ermittelbar, Berlin. (Reprinted in G. Lejeune Dirichlet’s Werke, Chelsea Publishing Company, New York, 1969).

has been cited by the following article:

• 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.