MathDB

Three conditions of the two variable function f

Source: Baltic Way 1998

January 11, 2011

functionnumber theory proposednumber theory

Problem Statement

Find all functions

f

of two variables, whose arguments

x,y

and values

f(x,y)

are positive integers, satisfying the following conditions (for all positive integers

x

and

y

): \begin{align*} f(x,x)& =x,\\ f(x,y)& =f(y,x),\\ (x+y)f(x,y)& =yf(x,x+y).\end{align*}