Fibonacci and Lucas numbers and their generalization have many interesting
properties and applications in almost every field of science and art. For
the prettiness and rich applications of these numbers and their relatives one
can see science and the nature [1,3] and [7-9].
In [5], M. Farrokhi gives some sufficient conditions on a natural number k
such that the equation Fn = kFm is solvable with respect to the unknowns n
and m. M. Farrokhi also show that for k > 1 the equation Fn = kFm has at
most one solution (n, m).