What is a good source of questions on primitive roots and order?

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Does anyone know of any resources on questions on primitive roots and order of a modulo n? They need to be suitable for elementary number theory course. (These could be interesting results and challenging ones).

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There are a vast collection of elementary number theory textbooks out there filled to the brim with exercises. I suspect you would find more than you could use in something like Kenneth Rosen's Elementary Number Theory book, or perhaps Ireland and Rosen's Classical introduction to Modern Number Theory if you intend to pitch it slightly higher. If you have access to a university library, I suspect one of the elementary number theory texts there would have illustrative exercises on primitive roots.

You might also browse the tag here and see if something catches your eye.