MathDB

2

Part of 2014 Federal Competition For Advanced Students, P2

Problems(1)

functional in [1,oo) , f (x^2 -y^2) = f (xy)

Source: 45th Austrian Mathematical Olympiad National Competition (Final Round, part 2) 28 May 2014 p2

1/11/2020
Let SS be the set of all real numbers greater than or equal to 11. Determine all functionsf:S→S f: S \to S, so that for all real numbers x,y∈Sx ,y \in S with x2−y2∈Sx^2 -y^2 \in S the condition f(x2−y2)=f(xy)f (x^2 -y^2) = f (xy) is fulfilled.
functional equationalgebra