Question 31
Let $n$ be a natural number greater than 1. Prove that there exists a natural number $m$ greater than $n^{n}$ such that
$$
\frac{n^{m}-m^{n}}{n+m}
$$
is a natural number.
$$
\frac{n^{m}-m^{n}}{n+m}
$$
is a natural number.
MathNet 2016-part-05 — 184 problems (EN–VI) Question 31
Math Olympiad Vault · MathNet 2016-part-05 — 184 problems (EN–VI)