For an odd prime, prove that a primitive root of $p^2$ is also a primitive root of $p^n$ for $n&gt;1$.  


I have proved the other way round that any primitive root of $p^n$ is also a primitive root of $p$ but I have not been able to solve this one. I have tried the usual things that is I have assumed the contrary that there does not exist the primitive root following the above condition and then proceeded but couldn't solve it.
Please help.


Question: Quick and dirty way to run a process more than once
Answer: Here is something that will launch your programs in parallel:

#!/bin/bash

count=$1
command=$2
shift 2

for ((i=0;i&lt;count;i++)); do
  $command "$@" &amp;
done
wait
echo done


The wait instruction should prevent zombies to show up. If your programs do not need a tty, you can replace the loop with:

for ((i=0;i&lt;count;i++)); do
  nohup $command "$@" &lt;/dev/null &gt;/dev/null 2&gt;&amp;1 &amp;
done


That way, the processes will be detached from your shell.