Question 100
Prove that there are only finitely many quadruples of positive integers $(a, b, c, n)$ for which the equality
$$
n! = a^{n-1} + b^{n-1} + c^{n-1}
$$
holds.
$$
n! = a^{n-1} + b^{n-1} + c^{n-1}
$$
holds.
MathNet 2022-part-05 — 197 problems (EN–VI) Question 100
Math Olympiad Vault · MathNet 2022-part-05 — 197 problems (EN–VI)