Abstract The k –generalized Fibonacci sequence (Fₘ^ (k) ) ₌ ₂-₊ (F m (k) ) m ≥ 2 - k is the linear recurrent sequence of order k whose first k terms are 0, , 0, 1 0, …, 0, 1 and each term afterwards is the sum of the preceding k terms. The case k=2 k = 2 corresponds to the well known Fibonacci sequence. In Gómez and Luca (Lith. Math. J. 56 (4): 503–517, 2016), the multiplicative independence between terms of the same k -generalized Fibonacci sequence was studied. In this paper, we find all the multiplicative dependent pairs (Fₘ^ (k), uₙ) (F m (k), u n) where uₙ u n is a Fibonacci, a Lucas or a Pell number.
Gomez et al. (Sat,) studied this question.