MathDB

[x,y,z] =(x,y)+(y,z) + (z,x) with x <= y <= z and (x,y,z) = 1

Source: China Northern MO 2010 p7 CNMO

May 4, 2024

number theoryLCMGCDleast common multiplegreatest common divisor

Problem Statement

Find all positive integers

x, y, z

that satisfy the conditions:

[x,y,z] =(x,y)+(y,z) + (z,x), x\le y\le z, (x,y,z) = 1

The symbols

[m,n]

and

(m,n)

respectively represent positive integers, the least common multiple and the greatest common divisor of

m

and

n