What are all possible functions on the reals that satisfy this functional equation?
$$f(x+f(x+y))+f(xy)=x+f(x+y)+yf(x)$$
source: http://www.imo2015.org/solution.php?lang=en

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Well... the identity function works for starters... :)

Haha yeah, the trouble is showing this is the only possible function.

really thats the only one?

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