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Firstly, $n=1,2$ give no solutions.
$$3^n+n^2+2019=k^2$$Notice: $k^2 \equiv n^2 \equiv 0,1 \pmod{3}$.
Tragedy of Bailey
Determine all the possible positive integer $n,$ such that $3^n+n^2+2019$ is a perfect square.
Number Theory
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