Abstract
The k-generalized Fibonacci and Pell polynomials are the polynomials X-k - Xk-1 - Xk-2 -center dot center dot center dot - 1 and X-k - 2X(k-1) - Xk-2 - center dot center dot center dot - 1, respectively. Here, k >= 2 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].