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 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.