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 …

A set of positive integers is called a Diophantine tuple if the product of any two elements in
the set increased by the unity is a perfect square. A conjecture on the regularity of …

A set of positive integers is called a Diophantine tuple if the product of any two elements in
the set increased by unity is a perfect square. Any Diophantine triple is conjectured to be …

This paper is a continuation of a recent paper (see [10]), in which for a fixed Diophantine pair
{a, b} with a< b, we gave an upper bound for minimal c such that {a, b, c, d} is an irregular …

Sažetak A set of m positive integers {a1,..., am} is called a Diophantine m-tuple if the product
of any two elements in the set increased by one is a perfect square. The conjecture …

A set of positive integers a1, a2,..., am with the property that aiaj+ 1 is a perfect square for all
distinct indices i and j between 1 and m is called Diophantine. In this paper, we show that if …

Let ε∈{±1} and let k be an integer such that k≥ 2 if ε=− 1 and k≥ 1 if ε= 1. For positive
integer d, we prove that if the product of any two distinct elements of the set {k, 4k+ 4ε …

There are no Diophantine quadruples of Pell numbers Page 1 International Journal of Number
Theory Vol. 18, No. 1 (2022) 27–45 c World Scientific Publishing Company DOI …

Sažetak The set of $ m $ positive integers with the property that the product of any two of
them increased by $4 $ is a perfect square is called a $ D (4) $-$ m $-tuple. In this paper we …

The purpose of the present paper is to consider the extensibility of the Diophantine triple {a,
b, c}, where a< b< c with b= 3 a, and to prove that such a set cannot be extended to an …