  let $R$ be a regular local ring of a mixed characteristic $(0,p)$ where
$p\neq 2$ is a prime number. Suppose that the quotient ring $R/pR$ is also
regular. Fix a non-degenerate Pfister form $Q(T_{1},\ldots,T_{2^{m}})$ over $R$
and an invertible element $c$ in $R$. Then the equation
$Q(T_{1},\ldots,T_{2^{m}})=c$ has a solution over $R$ if and only if it has a
solution over the fraction field $K$.

K-Theory and Homology