9 + 16 = 25 is one of them

\[n^2+(n+1)^2+\cdots +(n+k)^2=(n+k+1)^2+\cdots +(n+2k)^2\]

How many integers \(n\) with \(1\leq n \leq 2016\) are there such that the equation above is fulfilled for some positive integer \(k\)?

For example, with \(n=3,k=1\) we have the familiar Pythagorean triple \(3^2+4^2=5^2\).


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