Let  and be linear recurrence sequences.  It is a well-known Diophantine problem to decide the finiteness of the set of natural numbers such that their ratio is an integer.  In this paper we study an analogue of such a divisibility problem in the complex situation.

Namely,

we are concerned with the divisibility problem (in the sense of complex entire functions) for two sequences and , where the and are nonconstant entire functions and the and are non-zero constants except that can be zero.  We will show that the set of natural numbers such that is an entire function is finite under the assumption that is not constant for any non-trivial index set .