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Thread: Looking for name of theorem

  1. #1
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    Looking for name of theorem

    Suppose $\displaystyle p$ is prime and $\displaystyle n$ is a positive integer with $\displaystyle n<p$. Then if $\displaystyle n$ is a primitive root modulo $\displaystyle p$ and modulo $\displaystyle p^2$, then $\displaystyle n$ is a primitive root modulo $\displaystyle p^k$ for all positive integers $\displaystyle k$. I am sure I have seen this somewhere, but I can't for the life of me remember where. If I can't find it (and no one here knows its name), I will try to prove it (or disprove it if I am remembering it incorrectly).
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  2. #2
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    Re: Looking for name of theorem

    It's called theorem 8.9 in Rosen, Elementary Number Theory and it's Applications :P

    It seems to be called the primitive root theorem
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  3. #3
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    Re: Looking for name of theorem

    Awesome! Thank you very much. I don't have that text, but I found it at the library.
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