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Functional equation over reals

Source: Indian IMOTC 2013, Team Selection Test 2, Problem 1

July 30, 2013
functioninductionlimitalgebra proposedalgebraCauchy equation

Problem Statement

Find all functions ff from the set of real numbers to itself satisfying f(x(1+y))=f(x)(1+f(y)) f(x(1+y)) = f(x)(1 + f(y)) for all real numbers x,yx, y.
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