Products of Fibonacci numbers with indices in an interval and at most four omitted being a power (Q633038)

Let \((F_n)_{n\geq 0}\) be the Fibonacci numbers. Let \(n\geq 1\), \(k\geq 5\) and \({\mathcal I}\subseteq\{n,n+1,\dots,n+k-1\} \) such that \(|{\mathcal I}|\geq k-4\) and \[ \prod_{i\in{\mathcal I} }F_i=y^m \] holds with some integers \(y\) and \(m\geq 2\). The authors prove that \[ {\mathcal I}\in \{\{1\},\{2\},\{6\},\{12\},\{1,2\},\{1,6\},\{2,6\},\{3,6\},\{1,2,6\},\{1,3,6\},\{2,3,6\},\{1,2,3,6\}\}. \]