Problem

Source: INAMO 2019 P5

Tags: Inamo, algebra



Given that $a$ and $b$ are real numbers such that for infinitely many positive integers $m$ and $n$, \[ \lfloor an + b \rfloor \ge \lfloor a + bn \rfloor \]\[ \lfloor a + bm \rfloor \ge \lfloor am + b \rfloor \]Prove that $a = b$.