Abstract: Considering the first part of the Hilbert’s seventh
problem “irrationality (and transcendence) of certain numbers”, Duverney
obtains to be an irrational number for a
Fibonacci sequence In this paper, we obtain a
sufficient condition for which is an irrational number, where is a
solution of a linear difference equation with constant coefficients.
Keywords and phrases: Fibonacci sequences, Hilbert’s 7th problem, difference equations.
