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determine a real function of two integer variables

Source: RMO District 2005, 10th Grade, Problem 2

March 5, 2005
functionalgebra proposedalgebra

Problem Statement

Find the functions f:Z×Z→Rf:\mathbb{Z}\times \mathbb{Z}\to\mathbb{R} such that a) f(x,y)⋅f(y,z)⋅f(z,x)=1f(x,y)\cdot f(y,z) \cdot f(z,x) = 1 for all integers x,y,zx,y,z; b) f(x+1,x)=2f(x+1,x)=2 for all integers xx.
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