  Let $p$ be a nonconstant form in $\mathbb{R}[x_1,\dots,x_n]$ with
$p(1,\dots,1)>0$. If $p^m$ has strictly positive coefficients for some integer
$m\ge1$, we show that $p^m$ has strictly positive coefficients for all
sufficiently large $m$. More generally, for any such $p$, and any form $q$ that
is strictly positive on $(\mathbb{R}_+)^n\setminus\{0\}$, we show that the form
$p^mq$ has strictly positive coefficients for all sufficiently large $m$. This
result can be considered as a strict Positivstellensatz for forms relative to
$(\mathbb{R}_+)^n\setminus\{0\}$. We give two proofs, one based on results of
Handelman, the other on techniques from real algebra.
