Find the largest positive integer n such that \frac{(n + 1)^2}{n + 2} is an integer.
(n + 1)^2 = n^2 + 2n + 1
n
n + 2 [ n^2 + 2n + 1 ]
n^2 + 2n
___________
1
Note that this will never produce an integer because we will always have a remainder of 1 / (n + 2)
+2669 
