For the k-generalized Pell sequence defined by the given recurrence, the only multiplicatively dependent pairs P_n^(k) and P_m^(k) occur for small listed values of k, m, n.
Kili¸ c, The Binet formula, sums and representations of generalized Fibonacci p-numbers,European J
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Multiplicative independence in the sequence of $k$-generalized Pell numbers
For the k-generalized Pell sequence defined by the given recurrence, the only multiplicatively dependent pairs P_n^(k) and P_m^(k) occur for small listed values of k, m, n.