Algebraic $K$-theory and sums-of-squares formulas

Abstract

We prove a result about the existence of certain 'sums-of-squares' formulas over a field $F$. A classical theorem uses topological $K$-theory to show that if such a formula exists over $\mathbb{R}$, then certain powers of 2 must divide certain binomial coefficients. In this paper we use algebraic $K$-theory to extend the result to all fields not of characteristic 2.