[Number Theory] primitive root of prime powers

I had asked this question a long time back in sci.math.research but got
no response. So I am widening the audience in the hope that someone
will be able to help me out.

Artin's Conjecture states that given any squarefree a, we can find
infinitely many primes p such that a is a primitive root of p.

My question: Given a squarefree a, can we find _one_ prime p such that
a is a primitive root of p^2? (Just one such p is enough!). Is there
any known proof/counterexample?

Any references will be greatly appreciated.

Thanks.

.

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