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: What is the exact word used for this unusual "interval" of sorts?
Answer: I don't have a clear understanding of the phenomenon you are attempting to describe, but imagine at least the first of the following is relevant:

• caesura, “A pause or interruption in a poem, music, building or other work of art”  (Also see 2)
• lapse, “A pause in continuity”, “An interval of time between events”
• interruption, “A time interval during which there is a cessation of something”