Problem #PRU-61111

Problems Calculus Real numbers Integer and fractional parts. Archimedean property
 13–15  3.0

Problem

Let \(a, b\) be positive integers and \((a, b) = 1\). Prove that the quantity cannot be a real number except in the following cases \((a, b) = (1, 1)\), \((1,3)\), \((3,1)\).