  We derive an infinite hierarchy of exact equations for the Bak-Sneppen model
in arbitrary dimensions. These equations relate different moments of temporal
duration and spatial size of avalanches. We prove that the exponents of the BS
model are the same above and below the critical point and express the universal
amplitude ratio of the avalanche spatial size in terms of the critical
exponents. The equations uniquely determine the shape of the scaling function
of the avalanche distribution. It is suggested that in the BS model there is
only one independent critical exponent.
