RO-NMO 2010 Problem 81

Let $a,b,c$ be integers larger than $1$ . Prove that $a(a-1)+b(b-1)+c(c-1)\le (a+b+c-4)(a+b+c-5)+4.$

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.