In this study, we give some new identities concerning Fibonacci and Lucas numbers. I think
the identities we present here will be found fascinating. Then we present some Diophantine
equations such as z
2 + x
2 + y
2 = xyz + 4For a history of the Fibonacci numbers we refer the
reader to the reference [1]. For more information about Fibonacci and Lucas numbers one can
consult [6], [8], and [2].