We prove that there exist infinitely many rationals a, b and c with the property that [a^2-1, b^2-1, c^2-1, ab-1, ac-1] and [bc-1] are all perfect squares. This provides a solution to a variant of the problem studied by Diophantus and Euler
In this paper we prove that there does not exist a set of four non-zero polynomials from (mathbb{Z}[...
AbstractA set of m positive integers is called a Diophantine m-tuple if the product of its any two d...
Let n be a nonzero integer. A set of m distinct positive integers is called a D(n)-m-tuple if the pr...
We prove that there exist infinitely many rationals a, b and c with the property that [a^2-1, b^2-1,...
We show that for infinitely many square-free integers q there exist infinitely many triples of ratio...
We consider the problem of finding four different rational squares, such that the product of any two...
Rational Diophantine triples, i.e. rationals a, b, c with the property that ab + 1, ac + 1, bc + 1 a...
A rational Diophantine triple is a set of three nonzero rational (a,b,c) with the property that $ab+...
For a nonzero integer n, a set of distinct nonzero integers {a_{1} : a_{2} : a_{m}} such that a_{i}a...
In this paper we prove that every Diophantine quadruple in ℝ [X] is regular. In other words, we prov...
Quadruples (a; b; c; d) of positive integers a < b < c < d with the property that the product of any...
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...
AbstractLet q be a nonzero rational number. We investigate for which q there are infinitely many set...
A set {a1, ... ,am} of m distinct positive integers is called a Diophantine m-tuple if aiaj+1 is a p...
In this paper we prove that there does not exist a set of four non-zero polynomials from (mathbb{Z}[...
AbstractA set of m positive integers is called a Diophantine m-tuple if the product of its any two d...
Let n be a nonzero integer. A set of m distinct positive integers is called a D(n)-m-tuple if the pr...
We prove that there exist infinitely many rationals a, b and c with the property that [a^2-1, b^2-1,...
We show that for infinitely many square-free integers q there exist infinitely many triples of ratio...
We consider the problem of finding four different rational squares, such that the product of any two...
Rational Diophantine triples, i.e. rationals a, b, c with the property that ab + 1, ac + 1, bc + 1 a...
A rational Diophantine triple is a set of three nonzero rational (a,b,c) with the property that $ab+...
For a nonzero integer n, a set of distinct nonzero integers {a_{1} : a_{2} : a_{m}} such that a_{i}a...
In this paper we prove that every Diophantine quadruple in ℝ [X] is regular. In other words, we prov...
Quadruples (a; b; c; d) of positive integers a < b < c < d with the property that the product of any...
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...
AbstractLet q be a nonzero rational number. We investigate for which q there are infinitely many set...
A set {a1, ... ,am} of m distinct positive integers is called a Diophantine m-tuple if aiaj+1 is a p...
In this paper we prove that there does not exist a set of four non-zero polynomials from (mathbb{Z}[...
AbstractA set of m positive integers is called a Diophantine m-tuple if the product of its any two d...
Let n be a nonzero integer. A set of m distinct positive integers is called a D(n)-m-tuple if the pr...
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