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Finitely many x such that f(x)=1 functional equation

Source: Italy TST 2002

November 9, 2010
functionalgebra unsolvedalgebra

Problem Statement

Find all functions f:R+ā†’R+f:\mathbb{R}^+\rightarrow\mathbb{R}^+ which satisfy the following conditions: (i)(\text{i}) f(x+f(y))=f(x)f(y)f(x+f(y))=f(x)f(y) for all x,y>0;x,y>0; (ii)(\text{ii}) there are at most finitely many xx with f(x)=1f(x)=1.
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