Proof that, Sum of the squares of $5$ consecutive positive numbers can not be a perfect square.
As far I did,
$(n-2)^2 + (n-1)^2+n^2 + (n+1^2) + (n+2)^2$
$=2(n^2+4) + 2(n^2 + 1) + n^2$
$=5(n^2 + 2)$
If we can proof that this is not a perfect square then we are done. But I don't know how to prove it.