Find all primes $p$,$q$ such that $p<q<2020$ and $frac{p^2+q^2+1}{pq+2}$

is an integer.

Any idea would be appreciated.

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# Find all primes $p$,$q$ such that $p<q<2020$ and $frac{p^2+q^2+1}{pq+2}$ is an integer.

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is an integer.

Any idea would be appreciated.

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