  This paper consists of three steps. In the first, we prove that the
Bekenstein-Hawking entropy is the unique expression of black hole entropy. Our
proof is constructed in the framework of thermodynamics without any statistical
discussion. In the second, intrinsic properties of quantum mechanics are shown,
which justify the Boltzmann formula to yield a unique entropy in statistical
mechanics. These properties clarify three conditions, one of which is necessary
and others are sufficient for the validity of Boltzmann formula. In the third,
by combining the above results, we find a reasonable suggestion from the
sufficient conditions that the potential of gravitational interaction among
microstates of underlying quantum gravity may not diverge to negative infinity
(such as Newtonian gravity) but is bounded below at a finite length scale. In
addition to that, from the necessary condition, the interaction has to be
repulsive within the finite length scale. The length scale should be Planck
size. Thus, quantum gravity may become repulsive at Planck length. Also, a
relation of these suggestions with action integral of gravity at semi-classical
level is given. These suggestions about quantum gravity are universal in the
sense that they are independent of any existing model of quantum gravity.
