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*} functionnumber theory proposednumber theory