MathDB

2

Part of 2023 IRN-SGP-TWN Friendly Math Competition

Problems(1)

What if FE met rectangles?

Source: 2023 IRN-SGP-TWN Friendly Math Competition P2

7/16/2023
Let f:R2ā†’R+f: \mathbb{R}^{2} \to \mathbb{R}^{+}such that for every rectangle ABCDA B C D one has
f(A)+f(C)=f(B)+f(D). f(A)+f(C)=f(B)+f(D).
Let KLMNK L M N be a quadrangle in the plane such that f(K)+f(M)=f(L)+f(N)f(K)+f(M)=f(L)+f(N), for each such function. Prove that KLMNK L M N is a rectangle.
Proposed by Navid.
functional equationalgebrageometry