IR-MO-R2 2019 Problem 3

$x_1,x_2,...,x_n>1$ are natural numbers and $n \geq 3$ Prove that : $(x_1x_2...x_n)^2 \ne x_1^3 + x_2^3 +...+x_n^3$

Dataset text AI-MO AoPS. Quoted with source.

Solutions

No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label.