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 …

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 …

A set of positive integers with the property that the product of any two of them is the
successor of a perfect square is called Diophantine D (− 1) D(-1)‐set. Such objects are …

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 …

In this paper the known upper bound 10^ 96 10 96 for the number of Diophantine quintuples
is reduced to 6.8 ⋅ 10^ 32 6.8· 10 32. The key ingredient for the improvement is that certain …

In this paper, we define ak-Diophantine m-tuple to be a set of m positive integers such that
the product of any k distinct positive integers is one less than a perfect square. We study …

Abstract AD (n)-m-tuple, where n is a non-zero integer, is a set of m distinct elements in a
commutative ring R such that the product of any two distinct elements plus n is a perfect …

For a nonzero integer n, a set of distinct nonzero integers {a 1, a 2,…, am} such that aia j+ n
is a perfect square for all 1≤ i< j≤ m, is called a Diophantine m-tuple with the property D (n) …

Let A and k be positive integers. We study the Diophantine quadruples. We prove that if d is
a positive integer such that the product of any two distinct elements of the set increased by 1 …

In this paper, we show that some parametric families of D (− 1)-triples cannot be extended to
D (− 1)-quadruples. Using this result, we further show that in each case of r= pk, r= 2 pk, r 2+ …