  The AJ conjecture, formulated by Garoufalidis, relates the A-polynomial and
the colored Jones polynomial of a knot in the 3-sphere. It has been confirmed
for all torus knots, some classes of two-bridge knots and pretzel knots, and
most cabled knots over torus knots. The strong AJ conjecture, formulated by
Sikora, relates the A-ideal and the colored Jones polynomial of a knot. It was
confirmed for all torus knots. In this paper we confirm the strong AJ
conjecture for most cabled knots over torus knots.
