MathDB

symmetric, biadditive function

Source: miklos schweitzer 2005 q7

August 31, 2021

algebraSymmetricalgebraic number

Problem Statement

Let

t\in R

. Prove that

\exists A:R \times R \to R

such that A is a symmetric, biadditive, nonzero function and

A(tx,x)=0 \,\forall x\in R

iff t is transcendental or (t is algebraic and t,-t are conjugates over

\mathbb{Q}