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functional equation from R to R

Source: Romanian Nationals RMO 2005 - grade 9, problem 2

March 31, 2005

functionLaTeXalgebra proposedalgebra

Problem Statement

Find all functions

f:\mathbb{R}\to\mathbb{R}

for which

x(f(x+1)-f(x)) = f(x),

for all

x\in\mathbb{R}

and

| f(x) - f(y) | \leq |x-y| ,

for all

x,y\in\mathbb{R}

. Mihai Piticari