Question 8
The function $f$, defined on the set of ordered pairs of positive integers, satisfies the following properties for all positive integers $x,y$:
$$\begin{gathered}f(x,x)=x,\\
f(x,y)=f(y,x),\\
(x+y)f(x,y)=yf(x,x+y).\end{gathered}$$
Calculate $f(14,52)$.
$$\begin{gathered}f(x,x)=x,\\
f(x,y)=f(y,x),\\
(x+y)f(x,y)=yf(x,x+y).\end{gathered}$$
Calculate $f(14,52)$.