BALKAN-SL 2013 A6

Let $S$ be the set of positive real numbers. Find all functions $f\colon S^3 \to S$ such that, for all positive real numbers $x$, $y$, $z$ and $k$, the following three conditions are satisfied:

(a) $xf(x,y,z) = zf(z,y,x)$,

(b) $f(x, ky, k^2z) = kf(x,y,z)$,

(c) $f(1, k, k+1) = k+1$.

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