Über die kleinste natürliche Zahl maximaler Ordnung modm

Abstract

modm. Ifm is natural,a an integer with (a, m)=1 put

$$\begin{gathered} {}^om(a): = min\{ h\left| {h \in \mathbb{N},} \right.a^h \equiv 1(modm)\} , \hfill \\ \psi (m): = \max \{ o_m (a)\left| a \right. \in \mathbb{Z},(a,m) = 1\} , \hfill \\ g(m): = \min \{ a\left| {a \in \mathbb{N},(a,m) = 1,o_m (a) = } \right.\psi (m)\} . \hfill \\ \end{gathered} $$

Form prime,g(m) is the least natural primitive root modm. We establish the estimation

$$\sum\limits_{m< x} {g(m)<< x^{1 + \varepsilon } .} $$