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 \(\lfloor a\rfloor, \lfloor 2a\rfloor, \dots , \lfloor Na\rfloor\) are all different, and the numbers \(\lfloor 1/a\rfloor, \lfloor 2/a\rfloor,\dots , \lfloor M/a\rfloor\) are also all different. Find all such \(a\).