  For a knot $K$ in $S^3$, the $sl_2$-colored Jones function $J_K(n)$ is a
sequence of Laurent polynomials in the variable $t$, which is known to satisfy
non-trivial linear recurrence relations. The operator corresponding to the
minimal linear recurrence relation is called the recurrence polynomial of $K$.
The AJ conjecture \cite{Ga04} states that when reducing $t=-1$, the recurrence
polynomial is essentially equal to the $A$-polynomial of $K$. In this paper we
consider a stronger version of the AJ conjecture, proposed by Sikora \cite{Si},
and confirm it for all torus knots.
