lean_workbook_plus_10700

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