This problem is related to the so-called Diophantine representation of a
sequence of integers, and for some results we refer to the papers
are linear combinations with rational coecients of the classical Fibonacci and
Lucas numbers: F0 = 0, F1 = 1, Fn+
This problem is related to the so-called Diophantine representation of a
sequence of integers, and for some results we refer to the papers of M.J.
DeLeon [3], V.E. Hoggatt, M. Bicknell-Johnson [6], J.P. Jones [7], [8], [9],
and W.L. McDaniel [11]. Also, it is connected to the Y.V. Matiyasevich and
J. Robertson way to solve the Hilbert's Tenth Problem, and it has applications to the problem of singlefold Diophantine representation of recursively enumerable
sets. In the recent paper of R. Keskin, N. Demiturk [10] the equations
x2