Main Article Content
On a cubic family of Thue equations involving Fibonacci numbers and powers of two
Abstract
In this paper we completely solve the family of parametrised Thue equations
X(X - FnY )(X - 2nY ) - Y3 = ± 1,
where Fn is the n-th Fibonacci number. In particular, for any integer n 3 the
Thue equation has only the trivial solutions (±1, 0), (0, ∓1), ∓(Fn,1), ∓(2n,1).
