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There are exactly four positive integers $n$ such that $\[\frac{(n + 1)^2}{n + 23}\]$ is an integer. Compute the largest such $n$.

Guest Mar 13, 2017
edited by Guest  Mar 13, 2017
edited by Guest  Mar 13, 2017
edited by Guest  Mar 13, 2017
 #1
avatar+7153 
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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.

hectictar  Mar 13, 2017

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