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Find all functions $f:\mathbb{R} \to \mathbb{R}$, that are continuous at the point $x=0$ and satisfy:

$$f (x+y)=f (x)+f (y)+xy (x+y) \ \ \forall x,y \in \mathbb{R} $$

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    Well, f(x) = (x^3)/3 satisfies the functional equation and is continuous at 0.2010-11-12
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    btw, Mirzodaler: I am guessing you are just posting some interesting challenge problems you have come across. Please try to provide the source of the problems, whenever you can.2010-11-12

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