Add to ORKGt square then there exists an infinite number of Diophantine quadruples with the property D(n). Precisely, for any set b} with the property D(n), where ab is not a perfect square, there exists an infinite number of Diophantine quadruples of the form b, c, d} with the property D(n). There are also some explicit formulas for Diophantine quadruples with the property D(l ) (see [7]). For example: + 1, l 1), 4l 1)(l 2)}. 2 # If n is an integer of the form n = 4k + 2, k Z, then there does not exist Diophantine quadruple with the property D(n) (see also [2]). 3 # If n 2 (mod 4) and n S = {-4, -3, -1, 3, 5, 8, 12, 20} then there exists at least one Diophantine quadruple with the property D(n) and if n S T , w...
We show that there are only finitely many Diophantine quadruples, that is, sets of four positive int...
We consider Diophantine quintuples {a,b,c,d,e}{a,b,c,d,e}. These are sets of distinct positive integ...
Abstract: Let n be an integer. A set of positive integers is said to have the property D(n) if the p...
In this paper we prove that every Diophantine quadruple in ℝ [X] is regular. In other words, we prov...
Abstract. In this paper, we prove that if {k − 1, k+ 1, 4k, d}, where k ∈ Z[i]\{0,±1}, d ∈ Z[i], is ...
In this paper we prove that if {a,b,c,d} is a set of four non-zero polynomials with integer coeffici...
In this paper, we prove that if {k-1, k+1, 4k, d}, where k Z[i] {0, ± 1}, d Z[i], is a Diophantine ...
Let $z$ be an element of a commutative ring $R$. A Diophantine quadruple with the property $D(z)$, o...
In this paper we prove that there does not exist a set of four non-zero polynomials from (mathbb{Z}[...
AbstractIn this paper, we prove that if {a,b,c,d} is a set of four non-zero polynomials with integer...
Abstract. A set {a1,..., am} of m distinct positive integers is called a Diophantine m-tuple if aiaj...
AbstractA set {a1,…,am} of m distinct positive integers is called a Diophantine m-tuple if aiaj+1 is...
This paper concerns with the study of construction of Diophantine quadruples such that the product o...
A set of m positive integers is called a Diophantine m-tuple if the product of its any two distinct ...
A Diophantine m-tuple is a set of {a1,..., am} of positive rational num-bers or integers such that a...
We show that there are only finitely many Diophantine quadruples, that is, sets of four positive int...
We consider Diophantine quintuples {a,b,c,d,e}{a,b,c,d,e}. These are sets of distinct positive integ...
Abstract: Let n be an integer. A set of positive integers is said to have the property D(n) if the p...
In this paper we prove that every Diophantine quadruple in ℝ [X] is regular. In other words, we prov...
Abstract. In this paper, we prove that if {k − 1, k+ 1, 4k, d}, where k ∈ Z[i]\{0,±1}, d ∈ Z[i], is ...
In this paper we prove that if {a,b,c,d} is a set of four non-zero polynomials with integer coeffici...
In this paper, we prove that if {k-1, k+1, 4k, d}, where k Z[i] {0, ± 1}, d Z[i], is a Diophantine ...
Let $z$ be an element of a commutative ring $R$. A Diophantine quadruple with the property $D(z)$, o...
In this paper we prove that there does not exist a set of four non-zero polynomials from (mathbb{Z}[...
AbstractIn this paper, we prove that if {a,b,c,d} is a set of four non-zero polynomials with integer...
Abstract. A set {a1,..., am} of m distinct positive integers is called a Diophantine m-tuple if aiaj...
AbstractA set {a1,…,am} of m distinct positive integers is called a Diophantine m-tuple if aiaj+1 is...
This paper concerns with the study of construction of Diophantine quadruples such that the product o...
A set of m positive integers is called a Diophantine m-tuple if the product of its any two distinct ...
A Diophantine m-tuple is a set of {a1,..., am} of positive rational num-bers or integers such that a...
We show that there are only finitely many Diophantine quadruples, that is, sets of four positive int...
We consider Diophantine quintuples {a,b,c,d,e}{a,b,c,d,e}. These are sets of distinct positive integ...
Abstract: Let n be an integer. A set of positive integers is said to have the property D(n) if the p...