Tbilisi Mathematical Journal

Fibonacci numbers which are products of two Jacobsthal numbers

F. Erduvan, R. Keskin

In this paper, we find all Fibonacci numbers which are products of two Jacobsthal numbers. Also we find all Jacobsthal numbers which are products of two Fibonacci numbers. More generally, taking k,m,n as positive integers, it is proved that F_k=J_mJ_n implies that
(k,m,n) = (1,1,1), (2,1,1), (1,1,2), (2,1,2), (1,2,2), (2,2,2), (4,1,3), (4,2,3), (5,1,4), (5,2,4), (10,4,5), (8,1,6), (8,2,6)
and J_k=F_mF_k implies that
(k,m,n) = (1,1,1), (2,1,1), (1,2,1), (2,2,1), (1,2,2), (2,2,2), (3,4,1), (3,4,2), (4,5,1), (4,5,2), (6,8,1), (6,8,2).


Tbilisi Mathematical Journal, Vol. 14(2) (2021), pp. 105-116