On the diophantine equation x(n)-1/x-1=y(q), II

We announce several new theorems on the Diophantine equation (x(n) - 1)/(x - 1) = y(q), which include the fact that any integer greater than 2 and wit h all digits equal to 1 in base ten cannot be a pure power. We then apply t hese results to solve this equation for any integer x of the form x = z(t) with 2 less than or equal to z less than or equal to 10000 and t greater th an or equal to 1. (C) Academie des Sciences/Elsevier, Paris.