The largest value of $n$ such that $n+10| n^3+100$ If $n\in \mathbb{Z}$ and follow the property
$$n+10| n^3+100$$
then what is the largest value of $n$
Please help me to solve this!!!

Notice that: $n+10| n^3+100$ is same as $$n+10| n^3+1000-900$$
$$\implies n+10| (n^3+1000)-900$$
$$\implies n+10| (n+10)(n^2-10n+100)-900\implies n+10|900$$.
The greatest integer dividing $900$ is $900$ itself. So, for maximum $n$, $$n+10=900\implies n=900-10=890$$
