Find the smallest possible value
Source: All Russian Mathematical Olympiad 2008. 11.2
June 13, 2008
ratioalgebra proposedalgebra
Problem Statement
Petya and Vasya are given equal sets of weights, in which the masses of any two weights are in ratio at most . Petya succeeded to divide his set into groups of equal masses, while Vasya succeeded to divide his set into groups of equal masses. Find the smallest possible .