Competition problem — Number theory

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Number theory Difficulty 6.2 National olympiad Prove it

29. If $m$ has a primitive root $g$ , then
$g^{k}, \quad 1 \leqslant k \leqslant \varphi(m),(k, \varphi(m))=1$

are pairwise incongruent modulo $m$ and are all the primitive roots modulo $m$ , the number of which is $\varphi(\varphi(m))$ .

Solution

29. Derived from property $\mathbb{I}$ .

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Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.