I have the following expression for $n>3$:
$\frac{5\cdot(n-1)\cdot[8\cdot\operatorname{Luc}(n) + 5\cdot\operatorname{Luc}(n-1)] + [4\cdot\operatorname{Luc}(n-1) - 8\cdot\operatorname{Luc}(n)]}{25}$
where $\operatorname{Luc}(n)$ gives the $n$th term in the Lucas sequence
$ 2, 1, 3, 4, 7, 11, 18, 29, 47, 76, \dots $starting from index $0$.
How do I reduce/rearrange it to remove the $25$ from the denominator? I need this so that I can take the modulus of the entire equation, without first doing any division. (The number in the numerator exceeds $2^{64}$, and I cannot store it in the memory)