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Zbl 0868.11055
Glasby, S.P.
Generators for the group of units of $\bbfZ\sb n$. (English)
[J] Aust. Math. Soc. Gaz. 22, No.5, 226-228 (1995). ISSN 0311-0729

For a given integer, $n$, let $U_n$ denote the group of $k$ for which $(k,n)=1$. (The author's nomenclature is somewhat different.) For prime $p$, various theorems are given which relate the generators of $U_{p^i}$ to those of $U_p$, and these are used to obtain generators for $U_n$. \par An interesting byproduct is that if $a_p$ is the least primitive root modulo $p$, then $$\text{ord}_{p^2}(a_p)= p(p-1)$$ for all odd $p<10^7$, with the single exception $p=40487$.
[H.J.Godwin (Egham)]

MSC 2000:: *11R99 Algebraic number theory over global fields
11A07 Congruences, etc.

Keywords: group of units; primitive roots; generators

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