On a variant of Pillai's problem with factorials and S-units.

Let S be a finite, fixed set of primes. In this paper, we show that the set of integers c which have at least two representations as a difference between a factorial and an S-unit is finite and effectively computable. In particular, we find all integers that can be written in at least two ways as a difference of a factorial and an S-unit associated with the set of primes { 2 , 3 , 5 , 7 } . [ABSTRACT FROM AUTHOR]