MathDB

(a^3 + b^3 + c^3)/3 >= abc + a + b + c for pairwise different naturals

Source: 2021 Austrian Federal Competition For Advanced Students, Part 2, p1

June 6, 2021

inequalitiesalgebraAZE CMO TSTAZE EGMO TST

Problem Statement

Let

a, b

and

c

be pairwise different natural numbers. Prove

\frac{a^3 + b^3 + c^3}{3} \ge abc + a + b + c

. When does equality holds?
(Karl Czakler)