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Is there any primitive root of $p$ which is not primitive root of $p^2$ without $1$ (since $1$ is a primitive root of $2$ but $1$ is not a primitive root of $4$)?

Are there other examples?

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closed as off-topic by Scientifica, Parcly Taxel, max_zorn, jgon, Namaste Nov 18 '18 at 11:18

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If $a$ is a primitive root modulo $p$, then $a^p$ is also a primitive root modulo $p$ but not modulo $p^2$.

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