Proof of a generator for coprime integers
By Emma Payne •
Take the integers coprime to $p$ (all but multiples of $p$). Does there always exist an integer (generator) $a$ coprime to $p$ that generates the entire group of coprime integers under powers of $a$?
For example $3^k\equiv 3, 2, 6, 4, 5, 1 \mod 7$ therefore $3$ is the generator of the group because it generates all coprime integers.
I'm not to familar with group theory, so I don't know where to start, any hints? Or maybe its more advanced than I think.
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