  In order to study the Yamabe changing-sign problem, Bahri and Xu proposed a
conjecture which is a universal inequality for $p$ points in $\mathbb R^m$.
They have verified the conjecture for $p\leq3$. In this paper, we first
simplify this conjecture by giving two sufficient and necessary conditions
inductively. Then we prove the conjecture for the basic case $m=1$ with
arbitrary $p$. In addition, for the cases when $p=4,5$ and $m\geq2$, we manage
to reduce them to the basic case $m=1$ and thus prove them as well.
