On Tribonacci numbers written as a product of two Perrin numbers

In this paper, we give all solutions of the Diophantine equation [Formula: see text], where [Formula: see text] x [Formula: see text] x [Formula: see text], [Formula: see text] is the Perrin sequence, and [Formula: see text] is the Tribonacci sequence. We show that this Diophantine equation has only [Formula: see text] integer solution triples. For the proof, we use Baker’s method. Our motivation is to show that linear forms in logarithms can still be effectively used for the solutions of different Diophantine equations involving classical number sequences such as Fibonacci or Lucas sequences.