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: Is it usual for finished PhD students to send out physical copies of their thesis to unknown persons?
Answer: This varies by country and probably by field as well, which means I can only speak from my own experience in physics, in the US. What my experience says is that it is exceptionally rare to do this. Typically, a student will have one copy of their thesis printed and bound for their adviser, one for themselves, one or two for the university library if required by policy, and perhaps one or two for the student's parents, if they're interested. Each one of these copies costs $50 or more, and costs are borne by the student, so there is a large incentive to print as few copies as necessary.

More recently (in the past few years), I believe a lot of universities have switched to electronic archival of theses, which means the campus library no longer requires a printed copy. In these cases, a finalized PhD thesis might never get printed at all, depending on the preferences of the student and the adviser.

Certainly, to me, it is unheard of to send unsolicited printed copies of the thesis to other researchers. Of course, in physics some PhD theses are uploaded to arXiv for electronic distribution, so interested researchers can get access to them that way.