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Functional equation on R

Source: IMO ShortList 2003, algebra problem 2

September 30, 2004
functionalgebrafunctional equationIMO Shortlist

Problem Statement

Find all nondecreasing functions f:R→Rf: \mathbb{R}\rightarrow\mathbb{R} such that (i) f(0)=0,f(1)=1;f(0) = 0, f(1) = 1; (ii) f(a)+f(b)=f(a)f(b)+f(a+b−ab)f(a) + f(b) = f(a)f(b) + f(a + b - ab) for all real numbers a,ba, b such that a<1<ba < 1 < b.
Proposed by A. Di Pisquale & D. Matthews, Australia
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