MathDB

7

Part of 2005 Miklós Schweitzer

Problems(1)

symmetric, biadditive function

Source: miklos schweitzer 2005 q7

8/31/2021
Let t∈Rt\in R. Prove that ∃A:R×R→R\exists A:R \times R \to R such that A is a symmetric, biadditive, nonzero function and A(tx,x)=0 ∀x∈RA(tx,x)=0 \,\forall x\in R iff t is transcendental or (t is algebraic and t,-t are conjugates over Q\mathbb{Q}).
algebraSymmetricalgebraic number