On a Variant of an Identity Relating Cubes of Three Consecutive Fibonacci Numbers

Fn+13+Fn3-Fn-13=F3n, for all n≥ 1 , is a well-known identity fulfilled by the Fibonacci numbers. In this paper, we study a variant of this identity, replacing the cubic powers by a general power on the left–hand side and allowing an additional unknown exponent on the right–hand side.