Algebraic $K$-Theory and Sums-of-Squares Formulas

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 $2$.

2000 Mathematics Subject Classification:

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