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I'm trying to solve this problem from a highschool math competition:

Find all functions f : R → R such that, f(f(x+y)-f(x-y))=xy, for all real x,y.

Any ideas of how to approach it.

I have found that f(0)=0, if x=y f(f(2x))=x^2

Find all functions f : R → R such that, f(f(x+y)-f(x-y))=xy, for all real x,y.

Any ideas of how to approach it.

I have found that f(0)=0, if x=y f(f(2x))=x^2