Problem #PRU-35708

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

13–15 3.0

Problem

The positive irrational numbers $a$ and $b$ are such that $1 / a + 1 / b = 1$ . Prove that among the numbers $⌊ m a ⌋, ⌊ n b ⌋$ each natural number occurs exactly once.

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