1
$\begingroup$

if $n$ be positive integers,and such

(1):$$\prod_{1\le i\le n,(i,n)=1}i\equiv -1\pmod n$$ (2):there exsit $a,$ such $a$ is a primitive root modulo $n$.

show that $(1)\Longleftrightarrow (2)$

his problem comes from the fact that when I deal with other problem,and I can't prove it,Thanks

$\endgroup$

closed as off-topic by Carl Mummert, Alexander Gruber Feb 25 at 7:19

This question appears to be off-topic. The users who voted to close gave this specific reason:

  • "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Carl Mummert, Alexander Gruber
If this question can be reworded to fit the rules in the help center, please edit the question.

  • $\begingroup$ Related 1,2. A cyclic group of an even order has a single element of order two. $\endgroup$ – Jyrki Lahtonen Feb 9 at 14:14
  • $\begingroup$ Hello,have a simple methods to prove it? $\endgroup$ – inequality Feb 9 at 14:17