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Functional equation in three variables

Source: Balkan MO 2013, Problem 3

June 30, 2013
functionalgebradomainquadraticsalgebra proposed

Problem Statement

Let SS be the set of positive real numbers. Find all functions f ⁣:S3→Sf\colon S^3 \to S such that, for all positive real numbers xx, yy, zz and kk, the following three conditions are satisfied:
(a) xf(x,y,z)=zf(z,y,x)xf(x,y,z) = zf(z,y,x),
(b) f(x,ky,k2z)=kf(x,y,z)f(x, ky, k^2z) = kf(x,y,z),
(c) f(1,k,k+1)=k+1f(1, k, k+1) = k+1.
(United Kingdom)
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