On the distance between products of consecutive Fibonacci numbers and powers of Fibonacci numbers

Here, we find a lower bound for |Fn⋯Fn+k−1−Fmℓ| for positive integers k,ℓ,m and nn in terms of max{k,ℓ,m,n}max{k,ℓ,m,n}, where FsFs is the ssth Fibonacci number.