Monday, 10 March 2014

algebra precalculus - Functional equation with f(1) integer

Here is a nice problem: Let f:RR be a function, R is the set of real numbers, satisfying the following properties: f(1) is an integer and
xf(y)+yf(x)=(f(x+y))2f(x2)f(y2), for all x, y real numbers.
f(x)=0 is a solution, another is f(x)=x. These are all solutions?
better asking: determine all functions that satisfy the 2 conditions. I would like to see a complete solution! Thank you!

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