MathDB

Initially, two distinct positive integers

a

and

b

are written on a blackboard. At each step, Andrea picks two distinct numbers

x

and

y

on the blackboard and writes the number

gcd(x, y) + lcm(x, y)

on the blackboard as well. Let

n

be a positive integer. Prove that, regardless of the values of

a

and

b

, Andrea can perform a finite number of steps such that a multiple of

n

appears on the blackboard.

Problem Statement