Add to ORKGIn this paper, we first show that for any fixed D(-1)-triple {1,b,c} with b<c, there exist at most two d\u27s such that {1,b,c,d} is a D(-1)-quadruple with c<d. Using this result, we further show that there exist at most $10^{356}$ D(-1)-quadruples
Problems found in Diophantus's books on Arithmetics prompted intense research activity in recent yea...
A set of m positive integers {a1,...,am} is called a Diophantine m-tuple if the product of any two e...
A set of m positive integers {a1,...,am} is called a Diophantine m-tuple if the product of any two e...
In this paper, we first show that for any fixed D(-1)-triple {1,b,c} with b<c, there exist at most t...
Quadruples (a; b; c; d) of positive integers a < b < c < d with the property that the product of any...
A set of m distinct positive integers is called a D(-1)-m-tuple if the product of any distinct two e...
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 a nonzero integer. A set of m distinct positive integers is called a D(n)-m-tuple if the pr...
A set {a1, ... ,am} of m distinct positive integers is called a Diophantine m-tuple if aiaj+1 is a p...
For a nonzero integer n, a set of m distinct positive integers {a1, ... , am} is called a D(n)-m-tup...
In this paper we will significantly improve the known bound on the number of D(4)-quintuples, illust...
AbstractIn this paper, we consider the D(−1)-triple {1,k2+1,(k+1)2+1}. We extend the result obtained...
A D(-1)-quadruple is a set of positive integers {a, b, c, d}, with a r. A particular instance yields...
We consider Diophantine quintuples {a,b,c,d,e}. These are sets of positive integers, the product of ...
A set of m positive integers {a1,...,am} is called a Diophantine m-tuple if the product of any two e...
Problems found in Diophantus's books on Arithmetics prompted intense research activity in recent yea...
A set of m positive integers {a1,...,am} is called a Diophantine m-tuple if the product of any two e...
A set of m positive integers {a1,...,am} is called a Diophantine m-tuple if the product of any two e...
In this paper, we first show that for any fixed D(-1)-triple {1,b,c} with b<c, there exist at most t...
Quadruples (a; b; c; d) of positive integers a < b < c < d with the property that the product of any...
A set of m distinct positive integers is called a D(-1)-m-tuple if the product of any distinct two e...
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 a nonzero integer. A set of m distinct positive integers is called a D(n)-m-tuple if the pr...
A set {a1, ... ,am} of m distinct positive integers is called a Diophantine m-tuple if aiaj+1 is a p...
For a nonzero integer n, a set of m distinct positive integers {a1, ... , am} is called a D(n)-m-tup...
In this paper we will significantly improve the known bound on the number of D(4)-quintuples, illust...
AbstractIn this paper, we consider the D(−1)-triple {1,k2+1,(k+1)2+1}. We extend the result obtained...
A D(-1)-quadruple is a set of positive integers {a, b, c, d}, with a r. A particular instance yields...
We consider Diophantine quintuples {a,b,c,d,e}. These are sets of positive integers, the product of ...
A set of m positive integers {a1,...,am} is called a Diophantine m-tuple if the product of any two e...
Problems found in Diophantus's books on Arithmetics prompted intense research activity in recent yea...
A set of m positive integers {a1,...,am} is called a Diophantine m-tuple if the product of any two e...
A set of m positive integers {a1,...,am} is called a Diophantine m-tuple if the product of any two e...