Question

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

Answer 1

The answer is `890`.

Explanation:

This is an interesting question.

`p^3 + 100 = (p+10)(p^2-10p+100) - 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`.