MathDB

3

Part of 2013 Canadian Mathematical Olympiad Qualification Repechage

Problems(1)

lcm(y,z)=n

Source: Canadian Repêchage 2013: Problem 3

5/20/2014
A positive integer nn has the property that there are three positive integers x,y,zx, y, z such that lcm(x,y)=180\text{lcm}(x, y) = 180, lcm(x,z)=900\text{lcm}(x, z) = 900, and lcm(y,z)=n\text{lcm}(y, z) = n, where lcm\text{lcm} denotes the lowest common multiple. Determine the number of positive integers nn with this property.
number theoryleast common multiplenumber theory proposed