MathDB

2014 preRMO p11, gcd, xy = x + y + (x, y)

Source:

August 9, 2019

number theorygreatest common divisor

Problem Statement

For natural numbers

x \le y

and

y

, let

(x,y)

denote the greatest common divisor of

x

and

y

. How many pairs of natural numbers

x

and

y

with

x \le y

satisfy the equation

xy = x + y + (x, y)

?

Back to Problems View on AoPS