On Fermat and Mersenne numbers expressible as product of two k-Fibonacci numbers

Let k≥2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k\ge 2$$\end{document} be an integer. A generalization of the well-known Fibonacci sequence is the k-Fibonacci sequence. For this sequence, the first k terms are 0,…,0,1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$0,\ldots ,0,1$$\end{document} and each term afterwards is the sum of the preceding k terms. The goal of this paper is to investigate the Fermat and Mersenne numbers having representation as product of two k-Fibonacci numbers.