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Miklós Schweitzer 1957- Problem 5

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October 16, 2015
functional equationcollege contests

Problem Statement

5. Find the continuous solutions of the functional equation f(xyz)=f(x)+f(y)+f(z)f(xyz)= f(x)+f(y)+f(z) in the following cases:
(a) x,y,zx,y,z are arbitrary non-zero real numbers; (b) a<x,y,z<b(1<a3<b)a<x,y,z<b (1<a^{3}<b).
(R. 13)
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