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Difference between revisions of "2015 IMO Problems/Problem 5"

(Adding problem)
 
Line 2: Line 2:
 
<math>f(x+f(x+y))+f(xy) = x+f(x+y)+yf(x)</math>
 
<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>.
 
for all real numbers <math>x</math> and <math>y</math>.
 +
Proposed by Dorlir Ahmeti, Albania

Revision as of 15:00, 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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