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This contribution presents all possible solutions to the Diophantineequations $F_k=L_mL_n$ and $L_k=F_mF_n$. To be clear, Fibonacci numbers thatare the product of two arbitrary Lucas numbers and Lucas numbers that are theproduct of two arbitrary Fibonacci numbers are determined herein. The resultsunder consideration are proven by using Dujella-Peth\"o lemma in coordinationwith Matveev's theorem. All common terms of the Fibonacci and Lucas numbers aredetermined. Further, the Lucas-square Fibonacci and Fibonacci-square Lucasnumbers are given.

Fibonacci or Lucas numbers that are products of two Lucas numbers or two Fibonacci numbers