Sums of Factorials in Binary Recurrence Sequences Original Research Article

In this paper, we consider the problem of expressing a term of a given non-degenerate binary recurrence sequence as a sum of factorials. We show that if one bounds the number of factorials allowed, then there are only finitely many effectively computable terms which can be represented in this way. As an application, we also find the largest members of the classical Fibonacci and Lucas sequences which can be written as a sum or a difference of two factorials.