Using properties of the Steinberg character, we obtain a congruence modulo p for the number of
ways in which a p-regular element may be expressed as a commutator in a finite simple group G of Lie
type of characteristic p. This congruence shows that such an element is a commutator in G. We also
show that if K and L are conjugacy classes of G consisting of elements whose centralizers have order
relatively prime to p, then any p-regular element of G is expressible as the product of an element of K
and an element of L.