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the existence of function

Source: Indonesia IMO 2010 TST, Stage 1, Test 4, Problem 3

November 12, 2009

functionalgebra proposedalgebraFunction equations

Problem Statement

Determine all real numbers

a

such that there is a function

f: \mathbb{R} \rightarrow \mathbb{R}

satisfying x\plus{}f(y)\equal{}af(y\plus{}f(x)) for all real numbers

x

and

y

. Hery Susanto, Malang