All elements in the cyclic group C(n) = {g0 (= e), g, g2 ,, gn−1} are generated by a generator g . The number of generators of gi ,i∈S (n) of C(n) , namely S (n) is known to be Euler’s totient function ϕ (n) ; however, the average probability of an element being a generator has not been discussed before. Several analytic properties of ϕ (n) 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.
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