Find all $n \in \Bbb Z$ such that $n^2 + n + 1$ divide $n^3-22$ I need help with this problem:
Find all $n \in \Bbb Z$ such that $n^2 + n + 1$ divide $n^3-22$.
I've got to a point where I know that $n^2 + n + 1 | -21$. So it should be among {${-21, -7, -3, -1, 1, 3, 7, 21}$}.
How could I continue? Thanks

Check for all eight of these numbers whether they satisfy the given property. The ones that do are your solution.
