The $9_{35}$ divisibility conjecture for HOMFLY $F$-factors

Let $9_{35}$ be the pretzel knot under consideration. For each positive integer $i$, let $F_i$ be its $i$th $F$-factor and define

$$F_i'=A^2q^{2i}F_i.$$

The $9_{35}$ divisibility conjecture. For positive integers $i>1$,

$$(1+A^2q^{2(i-1)})\mid F_i+F'_{i-1}.$$

This divisibility has been verified in the paper for $2\leq i\leq 7$ and is proposed as a property of the $F$-factors for arbitrary positive $i$.