More fun in 2016, Part 4

Find the largest integer \(n\) such that \(n, n+2016\), and \(n-2016\) are all perfect squares.

Enter 666 if you come to the conclusion that no such \(n\) exists.

Bonus Question (very hard): Does there exist a rational number \(q\) such that \(q,q+2015\) and \(q-2015\) are all squares of rational numbers?

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