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We determine all integer triples (k, m, n) satisfying the Diophantine equations Pk = JmJn and Jk = PmPn, thereby characterizing Pell numbers that are products of two Jacobsthal numbers, and vice versa. In addition, we study the intersection of the Pell and Jacobsthal sequences and show that the only common values occur when m = 1, corresponding to the integers 1 and 5.
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Daşdemir et al. (2026) studied this question.
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