Let $ a $, $ b $, $ c $ be fixed coprime positive integers with $\min\{a, b, c\}> 1$. In this
survey, we consider some unsolved problems and related works concerning the positive …

The k-generalized Fibonacci sequence (F n (k)) n (sometimes also called k-bonacci or k-
step Fibonacci sequence), with k≥ 2, is defined by the values 0, 0,…, 0, 1 of starting k its …

This study reports an investigation of the Pell (or Mersenne) numbers that can be written in
terms of the summation of two random Mersenne (or Pell) numbers within the framework of …

Let (F n) n≥ 0 be the Fibonacci sequence given by F n+ 2= F n+ 1+ F n for n≥ 0, where F 0=
0 and F 1= 1. In this paper, we explicitly find all solutions of the title Diophantine equation …

An Exponential Diophantine Equation Related to Powers of Three Consecutive Fibonacci
Numbers | Bulletin of the Malaysian Mathematical Sciences Society Skip to main content …

Let (F_n) _ {n} be the classical Fibonacci sequence. It is well-known that it satisfies F_ {n}^
2+ F_ {n+ 1}^ 2= F_ {2n+ 1}. In this study, we explore generalizations of this Diophantine …

Let (F_n^{(k)}) _ {n\geq-(k-2)} be the k-generalized Fibonacci sequence, defined as the
linear recurrence sequence whose first k terms are\(0, 0,\ldots, 0, 1\), and whose subsequent …

This study presents all solutions to the Diophantine equations F_k= L_m L_n and L_k= F_m
F_n. To be clear, the Fibonacci numbers that are the product of two arbitrary Lucas numbers …

This contribution presents all possible solutions to the Diophantine equations $ F_k=
L_mL_n $ and $ L_k= F_mF_n $. To be clear, Fibonacci numbers that are the product of two …

In this paper, we explicitly find all solutions of the title Diophantine equation, using lower
bounds for linear forms in logarithms and properties of continued fractions. Further, we use a …