Abstract
AbstractLet 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 $$\{2,3,5,7\}$$ { 2 , 3 , 5 , 7 } .
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