On the Jacobsthal numbers which are the product of two Modified Pell numbers

Abstract

This paper presents an analytic study of determining all the possible solutions of the Diophantine equations such that $ {q_k} = {J_m} {J_n} $ and $ {J_k} = {q_m} {q_n} $. These give intersections of the Modified Pell and Jacobsthal numbers too for the case where $ m = 1 $ or $ n = 1 $.