  As an analogue of the Hadamard quotient problem in number theory, the
quotient problem (in the sense of complex entire functions) for two sequences
$F(n)=a_0+a_1f_1^n+\cdots+a_lf_l^n$ and $ G(n)=b_0+b_1g_1^n+\cdots+b_mg_m^n$,
has been solved, where the $f_i$ and $g_j$ are nonconstant entire functions and
$a_i$ and $b_j$ are non-zero constants except that $a_0$ can be zero. In this
paper, we consider the generalization of this problem in which we allow $a_i$
and $b_j$ to be small growth entire functions with respect to $(g_1, \cdots,
g_m)$ by modifying the second main theorem with moving targets to a truncated
version. We also compare our result to a special case in exponential
polynomials first studied by Ritt.
