Problem #PRU-78051

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

13–15 4.0

Problem

The numbers $⌊ a ⌋, ⌊ 2 a ⌋, \dots, ⌊ N a ⌋$ are all different, and the numbers $⌊ 1 / a ⌋, ⌊ 2 / a ⌋, \dots, ⌊ M / a ⌋$ are also all different. Find all such $a$ .

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