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


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

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  • $\begingroup$ 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