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Find all functions f from the set of real numbers into the set of real numbers which satisfy for all x, y the identity f\left(xf(x+y)\right) = f\left(yf(x)\right) +x^2

Proposed by Japan

Slični zadaci

1933IMO Shortlist 1996 problem A70
2124IMO Shortlist 2003 problem A51
2152IMO Shortlist 2004 problem A60
2269IMO Shortlist 2008 problem A63
2294IMO Shortlist 2009 problem A55
2422MEMO 2009 pojedinačno problem 111