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

n=1; a=((n+1)^2 / (n+23));printa, n; n++; if(n<500, goto1, 0)

The 4 numbers are: 21, 98, 219, 461

The largest n = 461