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How does knowing the factorization of N can help to obtain the secret?

Assuming $x=a^2 \pmod n$ and knowing $x$, $p$, $q$ how is it possible to obtain $a$?
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Zero Knowledge Non Interactive Proof with random oracle

I am trying to write an assay about Non Interactive Zero-Knowledge proofs and would like to take the simple discrete logarithm problem example fallowing the Feige-Fiat-Shamir heuristics. I understand ...