When is this a perfect square?

When is this a perfect square? Can you find all positive integer number n such that n²+n+2016 is a perfect square? Solve this viewer suggested number theory problem from the 2016 Singapore Junior Mathematical Olympiad!
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[@parthosaha4170]

The technique is often used to solve this type of problems and still the technique amazes me every time

[@sima5852]

we can write
n^2+n+2016 as n^2+2.n.1/2+1/4+8063/4
Maybe that's how we get the inspiration to multiply by 4