ABSTRACT
The kth powers of the Fibonacci numbers satisfy a linear homogeneous recurrence relation of order k + 1 with integer coefficients.
Let’s consider one of the most famous sequences of numbers, the Fibonacci sequence, named after Leonardo of Pisa, a.k.a. Leonardo Fibonacci (1170-1250). The Fibonacci sequence {F0, F1, F2, . . .} is defined recursively by the initial values
F0 = 0, F1 = 1,
and the recurrence relation
Fn = Fn−1 + Fn−2, for n ≥ 2.
