On the multiplicative independence of the roots of generalized Fibonacci and Pell polynomials

The [Formula: see text]-generalized Fibonacci and Pell polynomials are the polynomials [Formula: see text] and [Formula: see text], respectively. Here, [Formula: see text] is any integer. In this paper, we show that any two roots of some generalized Fibonacci and Pell polynomials are multiplicatively independent confirming a conjecture from [Bravo, Herrera and Luca, Common values of generalized Fibonacci and Pell sequences, J. Number Theory 226 (2021) 51–71].