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 …

High power diode lasers have enabled higher placement rates to be achieved in automated
tape placement (ATP) of thermoplastic-based composite materials. Laser ATP heads in …

Nonexistence of D(4)-quintuples - ScienceDirect Skip to main contentSkip to article Elsevier
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Diophantine m-tuples and elliptic curves Page 1 JOURNAL DE THÉORIE DES NOMBRES
DE BORDEAUX ANDREJ DUJELLA Diophantine m-tuples and elliptic curves Journal de …

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 …

We consider Diophantine quintuples $\{a, b, c, d, e\} $. These are sets of distinct positive
integers, the product of any two elements of which is one less than a perfect square. It is …

Let A and K be positive integers and є∈{− 2;− 1, 1, 2}. The main contribution of the paper is
a proof that each of the D (є 2)-triples {K, A 2 K+ 2 є A,(A+ 1) 2 K+ 2 є (A+ 1)} has unique …

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 …

In this paper, we prove that if {a 1, b, c, d} and {a 2, b, c, d} are Diophantine quadruples with
a 1< a 2< b< c< d, then a 2> 24 3, a 2> max {36 a 1 3, 300 a 1 2}, b< a 2 3/2, and 16 a 1 2 b …