MathDB
Summation function

Source: Romanian IMO Team Selection Test TST 1996, problem 7

September 24, 2005
functionalgebrapolynomialalgebra unsolved

Problem Statement

Let a∈R a\in \mathbb{R} and f1(x),f2(x),…,fn(x):R→R f_1(x),f_2(x),\ldots,f_n(x): \mathbb{R} \rightarrow \mathbb{R} are the additive functions such that for every x∈R x\in \mathbb{R} we have f1(x)f2(x)⋯fn(x)=axn f_1(x)f_2(x) \cdots f_n(x) =ax^n . Show that there exists b∈R b\in \mathbb {R} and i∈{1,2,…,n} i\in {\{1,2,\ldots,n}\} such that for every x∈R x\in \mathbb{R} we have fi(x)=bx f_i(x)=bx .
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