Problem #PRU-35708

Problems Methods Real numbers Integer and fractional parts. Archimedean property Pigeonhole principle (angles and lengths) Pigeonhole principle Calculus

Problem

The positive irrational numbers \(a\) and \(b\) are such that \(1/a + 1/b = 1\). Prove that among the numbers \(\lfloor ma\rfloor , \lfloor nb\rfloor\) each natural number occurs exactly once.