There are exactly four positive integers $n$ such that $\[\frac{(n + 1)^2}{n + 23}\]$ is an integer. Compute the largest such $n$.
I'm sorry I don't have an explanation, but I have an answer.
The four numbers are 21, 98, 219, and 461, so the largest is 461.
I found this by making a table and scrolling through to find all four of them.
