Add to ORKGAbstract. For a nonzero integer n, a set of m distinct positive inte-gers fa1; : : : ; amg is called a D(n)-m-tuple if aiaj + n is a perfect square for each i; j with 1 i < j m. Let k be an integer with jkj prime. Then we show that the D(4k)-triple f1; 4k(k 1); 4k2 + 1g cannot be extended to a D(4k)-quadruple. 1
AbstractA set {a1,…,am} of m distinct positive integers is called a Diophantine m-tuple if aiaj+1 is...
Diophantine 3-tuples with property P-k, for k an integer, are sets of n positive integers such that ...
This note gives a summary of the paper [M. Cipu, Y. Fujita, M. Mignotte, Two-parameter families of u...
For a nonzero integer n, a set of m distinct positive integers {a1, ... , am} is called a D(n)-m-tup...
Abstract. In this paper we prove that for an integer k such that jkj 2, the D(2k + 1)-triple f1; k2...
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 n be a nonzero integer. A set of m distinct positive integers is called a D(n)-m-tuple if the pr...
Abstract. In this paper, we prove that if {k − 1, k+ 1, 4k, d}, where k ∈ Z[i]\{0,±1}, d ∈ Z[i], is ...
Let n be a nonzero integer. A set of m distinct positive integers is called a D(n)-m-tuple if the pr...
Let n be an integer. A set of m positive integers is called a D(n)-m-tuple if the product of any two...
The set of $m$ positive integers with the property that the product of any two of them increased by ...
In this paper, we study the extensibility of the D(4)-triple {1, b, c}, where 1 < b < c, by proving ...
In this paper, we study the extensibility of the D(4)-triple {1, b, c}, where 1 < b < c, by proving ...
AbstractA set of m distinct positive integers {a1,…,am} is called a Diophantine m-tuple if aiaj+1 is...
Abstract. The D(−1)-quadruple conjecture states that there does not exist a set of four positive int...
AbstractA set {a1,…,am} of m distinct positive integers is called a Diophantine m-tuple if aiaj+1 is...
Diophantine 3-tuples with property P-k, for k an integer, are sets of n positive integers such that ...
This note gives a summary of the paper [M. Cipu, Y. Fujita, M. Mignotte, Two-parameter families of u...
For a nonzero integer n, a set of m distinct positive integers {a1, ... , am} is called a D(n)-m-tup...
Abstract. In this paper we prove that for an integer k such that jkj 2, the D(2k + 1)-triple f1; k2...
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 n be a nonzero integer. A set of m distinct positive integers is called a D(n)-m-tuple if the pr...
Abstract. In this paper, we prove that if {k − 1, k+ 1, 4k, d}, where k ∈ Z[i]\{0,±1}, d ∈ Z[i], is ...
Let n be a nonzero integer. A set of m distinct positive integers is called a D(n)-m-tuple if the pr...
Let n be an integer. A set of m positive integers is called a D(n)-m-tuple if the product of any two...
The set of $m$ positive integers with the property that the product of any two of them increased by ...
In this paper, we study the extensibility of the D(4)-triple {1, b, c}, where 1 < b < c, by proving ...
In this paper, we study the extensibility of the D(4)-triple {1, b, c}, where 1 < b < c, by proving ...
AbstractA set of m distinct positive integers {a1,…,am} is called a Diophantine m-tuple if aiaj+1 is...
Abstract. The D(−1)-quadruple conjecture states that there does not exist a set of four positive int...
AbstractA set {a1,…,am} of m distinct positive integers is called a Diophantine m-tuple if aiaj+1 is...
Diophantine 3-tuples with property P-k, for k an integer, are sets of n positive integers such that ...
This note gives a summary of the paper [M. Cipu, Y. Fujita, M. Mignotte, Two-parameter families of u...