+452 Find the largest positive integer n such that
\frac{(n + 1)^2}{n + 2}
is an integer.
+35 (n+1)^2/(n+2). Expanding, we have (n^2 + 2n + 1)/(n+2). By synthetic division, we have n + 1/(n+2). Now we want a positive integer n such that 1/(n+2) is an integer. This obviously cannot happen, we would need -1 to make 1/(n+2) an integer.
(Going off topic here), theoritically, if you take the limit as n approaches infinity, 1/(n+2) is 0 and you get infinity. I guess it would be divergent either way (awww).
Final answer is cannot happen, there isnt an n that can satisfy the given conditions.
