  In this paper we provide a version of the Floquet's theorem to be applied to
any second order difference equations with quasi-periodic coefficients. To do
this we extend to second order linear difference equations with quasi-periodic
coefficients, the known equivalence between the Chebyshev equations and the
second order linear difference equations with constant coefficients. So, any
second order linear difference equations with quasi-periodic coefficients is
essentially equivalent to a Chebyshev equation, whose parameter only depends on
the values of the quasi-periodic coefficients and can be determined by a
non-linear recurrence. Moreover, we solve this recurrence and obtaining a
closed expression for this parameter. As a by-product we also obtain a
Floquet's type result; that is, the necessary and sufficient condition for the
equation has quasi-periodic solutions.
