What is the largest positive $n$ for which $n^3+100$ is divisible by $n+10$ What is the largest positive $n$ for which $n^3+100$ is divisible by $n+10$
I tried to factorize $n^3+100$, but $100$ is not a perfect cube. I wish it were $1000$.

By division we find that $n^3 + 100 = (n + 10)(n^2 − 10n + 100)−900$. 
Therefore, if $n +10$ divides $n^3 +100$, then it must also divide $900$.
Since we are looking for largest $n$, $n$ is maximized whenever $n + 10$ is, and since the largest divisor of $900$ is $900$, we must have $n + 10 = 900 \Rightarrow n = 890$
The largest $n$ is therefore $890$
