On the p-divisibility of Fermat quotients

The authors carried out a numerical search for Fermat quotients Q(a) = (a(p - 1) - 1)/p, vanishing mod p, for 1 less than or equal to a less than or equal to p - 1, up to p < 10(6). This article reports on the results and surveys the associated theoretical properties of Q(a). The approach of fixing the prime p rather than the base a leads to some aspects of the theory apparently not published before.