On multiplicative dependent vectors with coordinates from certain higher order recurrences

In this paper, we prove that there are finitely many multiplicative dependent vectors with coordinates from non-degenerate linear recurrence sequences [Formula: see text] of a fixed order [Formula: see text] These sequences satisfy the recurrence relation [Formula: see text] with initials [Formula: see text] [Formula: see text]. Here, the coefficients of the recurrence relation are positive integers satisfying [Formula: see text] or [Formula: see text] In both these conditions, [Formula: see text]