A set of m positive integers is called a Diophantine m-tuple if the product of its any two
distinct elements increased by 1 is a perfect square. Diophantus found a set of four positive …

A set of $ m $ positive integers $\{a_1, a_2,\ldots, a_m\} $ is called a Diophantine $ m $-
tuple if $ a_i a_j+ 1$ is a perfect square for all $1\le i< j\le m $. Dujella proved that there is no …

When you ask different people what they like most about mathematics, you are likely to get
different answers: For some, it is the clarity and beauty of pure reasoning; for others, grand …

For an integer k 2, let. F. k/n/n be the k-Fibonacci sequence which starts with 0;:::; 0; 1 (k
terms) and each term afterwards is the sum of the k preceding terms. In this paper, we …

Teorija brojeva grana je matematike koja se ponajprije bavi proucavanjem svojstava
prirodnih brojeva kao što su djeljivost, rastav na proste faktore ili rješivost jednadžbi u …

The k-generalized Fibonacci sequence\big (Fn (k)\big) n resembles the Fibonacci sequence
in that it starts with 0,…, 0, 1 (k terms) and each term afterwards is the sum of the k preceding …

Number theory is a branch of mathematics that is primarily focused on the study of positive
integers, or natural numbers, and their properties such as divisibility, prime factorization, or …

Fibonacci numbers which are concatenations of two repdigits Page 1 Quaestiones
Mathematicae 2021, 44(2): 281–290 c⃝ 2019 NISC (Pty) Ltd https://doi.org/10.2989/16073606.2019.1686439 …

The extensibility of Diophantine pairs {k − 1,k + 1} Page 1 Journal of Number Theory 128 (2008)
322–353 www.elsevier.com/locate/jnt The extensibility of Diophantine pairs {k − 1,k + 1} …

In this paper, we find all the solutions of the title Diophantine equation in positive integer
variables (n, m, a), where F k is the k th term of the Fibonacci sequence. The proof of our …