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!!!

Note that
$$
n+10|n^3+10n^2\implies n+10|(n^3+10n^2)-(n^3+100)=10n^2-100.
$$
Similarly,
\begin{aligned}
&\quad n+10|(10n^2+100n)-(10n^2-100)=100n+100\\
&\implies n+10|(100n+1000)-(100n+100)=900.
\end{aligned}
So the largest possible $n$ is $900-10=\boxed{890}$. Verify that this works:
$$
\frac{890^3+100}{890+10}=783299\in\mathbb{Z}.
$$
