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**alexgeek101** Hi, I am having a tough time with this question.

Let $\displaystyle e$ and $\displaystyle f$ be primitive roots modulo an odd prime $\displaystyle p$ and let $\displaystyle a$ be an interger co-prime to p.

Using $\displaystyle a \equiv e^g \equiv f^h (mod \ p)$, prove $\displaystyle g \equiv h (mod \ 2)$.

Then show that $\displaystyle e^{p-2}$ is a primitive root modulo $\displaystyle p$.

For the first part I know that $\displaystyle g \equiv h (mod \ 2)$ means that $\displaystyle g$ and $\displaystyle h$ are either both odd or both even. But I need some help with this question.

Thank You for any help.