# Cool...!

Algebra Level 5

The function $$f$$ defined on the set of ordered pairs of positive integers has the following properties:

(a) For all $$x,$$ $$f(x,x) = x.$$

(b) For all $$x$$ and $$y,$$ $$f(x,y) = f(y,x).$$

(c) For all $$x$$ and $$y,$$ $$(x + y)f(x,y) = yf(x,x+y).$$

Find $$f(52,14).$$

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