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Special function on the integers

Source: Kürschak 2009, problem 3

July 8, 2014
functionalgebra unsolvedalgebra

Problem Statement

Find all functions f:Z→Qf:\mathbb{Z}\to \mathbb{Q} with the following properties: if f(x)<c<f(y)f(x)<c<f(y) for some rational cc, then ff takes on the value of cc, and f(x)+f(y)+f(z)=f(x)f(y)f(z)f(x)+f(y)+f(z)=f(x)f(y)f(z) whenever x+y+z=0x+y+z=0.
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