CMO 1972 Problem 6

Let $a$ and $b$ be distinct real numbers. Prove that there exist integers $m$ and $n$ such that $am+bn<0$ , $bm+an>0$ .

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.