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

### Daniel Dugger

### Daniel C. Isaksen

Department of Mathematics Department of Mathematics University of Oregon Wayne State University Eugene, OR 97403, USA Detroit, MI 48202, USA

## 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.

## Cite this article

Daniel Dugger, Daniel C. Isaksen, Algebraic $K$-theory and sums-of-squares formulas. Doc. Math. 10 (2005), pp. 357–366

DOI 10.4171/DM/192