The largest integer p for which p + 10 divides p^3 + 100?

Oct 12, 2015

The answer is $890$.

Explanation:

This is an interesting question.

${p}^{3} + 100 = \left(p + 10\right) \left({p}^{2} - 10 p + 100\right) - 900$

So if $p + 10$ is a divisor of ${p}^{3} + 100$, then it must also be a divisor of $- 900$.

The largest integer divisor of $- 900$ is $900$, yielding $p = 890$.