#### DOCUMENTA MATHEMATICA, Vol. 10 (2005), 357-366

Daniel Dugger, Daniel C. Isaksen

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:

Keywords and Phrases:

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