On multiplicative intersections between the Pell and Jacobsthal numbers

Abstract

We determine all integer triples ( k, m, n ) satisfying the Diophantine equations P _k = J _m J _n and J _k = P _m P _n , 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.