2015 IMO Problems/Problem 5: Difference between revisions

Revision as of 15:01, 4 April 2016

Let $\mathbb{R}$ be the set of real numbers. Determine all functions $f$ : $\mathbb{R}\rightarrow\mathbb{R}$ satisfying the equation

$f(x+f(x+y))+f(xy) = x+f(x+y)+yf(x)$

for all real numbers $x$ and $y$ .

Proposed by Dorlir Ahmeti, Albania

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 Let <math>\mathbb{R}</math> be the set of real numbers. Determine all functions <math>f</math>:<math>\mathbb{R}\rightarrow\mathbb{R}</math> satisfying the equation
 <math>f(x+f(x+y))+f(xy) = x+f(x+y)+yf(x)</math>
 for all real numbers <math>x</math> and <math>y</math>.
 Proposed by Dorlir Ahmeti, Albania