Question 60
Let $a$, $b$, $c$ be pairwise distinct natural numbers.
Prove that
$$
\frac{a^3 + b^3 + c^3}{3} \ge abc + a + b + c.
$$
When does equality hold?
Prove that
$$
\frac{a^3 + b^3 + c^3}{3} \ge abc + a + b + c.
$$
When does equality hold?
MathNet 2021 — Part 01 Question 60
Math Olympiad Vault · MathNet 2021 — Part 01