For what values of nnn does n2+n+1n−1\frac{n^2 + n + 1}{n - 1}n−1n2+n+1 yield an integer (for integer nnn, n≠1n \neq 1n=1)?
All integers n≠1n \neq 1n=1
Only n=0n = 0n=0 and n=2n = 2n=2
nnn such that (n−1)∣3(n - 1) \mid 3(n−1)∣3
No such integer exists