Timeline for Powers modulo a fixed integer

7 events

when toggle format	what		by	license	comment
May 4, 2015 at 18:16	vote	accept	Dominic van der Zypen
May 4, 2015 at 14:56	answer	added	so-called friend Don		timeline score: 8
May 4, 2015 at 14:49	comment	added	Emil Jeřábek		To expand on user35593’s comment: even if the requirements were loosened so that $\{1,\dots,c-1\}$ is replaced with $\{u<c:(u,c)=1\}$, $(\mathbb Z/c\mathbb Z)^\times$ is cyclic only for $c$ of the form $p^k$ or $2p^k$, so $S_b$ would still be of density $0$. The sensible question is to ask for relative density of $S_b$, in the primes, which more or less amounts to Artin’s primitive root conjecture.
May 4, 2015 at 14:28	history	edited	Dominic van der Zypen	CC BY-SA 3.0	edited body
May 4, 2015 at 14:27	comment	added	Dominic van der Zypen		Oh - typo... it should be $\{1,\ldots,c-1\}$. Thanks for pointing it out!
May 4, 2015 at 14:27	comment	added	user35593		If $c\in S_b$ it has to be coprime to $b$. By Euler's theorem $S_b$ can only contain primes. Hence by the prime number theorem $S_b$ has not positive measure.
May 4, 2015 at 14:14	history	asked	Dominic van der Zypen	CC BY-SA 3.0