1786 - 0091 on the Family of Diophantine Triples {
نویسندگان
چکیده
In this paper, we prove that if k and d are two positive integers such that the product of any two distinct elements of the set {k + 2, 4k, 9k + 6, d} increased by 4 is a perfect square, then d = 36k + 96k + 76k + 16.
منابع مشابه
On the family of Diophantine triples { k − 1 , k + 1 , 16 k 3 − 4 k }
It is proven that if k ≥ 2 is an integer and d is a positive integer such that the product of any two distinct elements of the set {k − 1, k + 1, 16k − 4k, d} increased by 1 is a perfect square, then d = 4k or d = 64k−48k+8k. Together with a recent result of Fujita, this shows that all Diophantine quadruples of the form {k − 1, k + 1, c, d} are regular.
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متن کاملOn the Rank of Elliptic Curves Coming from Rational Diophantine Triples
We construct a family of Diophantine triples {c1(t), c2(t), c3(t)} such that the elliptic curve over Q(t) induced by this triple, i.e.: y = (c1(t) x + 1)(c2(t) x + 1)(c3(t) x + 1) has torsion group isomorphic to Z/2Z× Z/2Z and rank 5. This represents an improvement of the result of A. Dujella, who showed a family of this kind with rank 4. By specialization we obtain two examples of elliptic cur...
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A complex algebra A is called ideally factored if Ia = Ca is a left ideal of A for all a ∈ A. In this article, we investigate some interesting properties of ideally factored algebras and show that these algebras are always Arens regular but never amenable. In addition, we investigate ρhomomorphisms and (ρ, τ)-derivations on ideally factored algebra.
متن کاملOn the number of Diophantine m-tuples
A set of m positive integers is called a Diophantine m-tuple if the product of any two of them is one less than a perfect square. It is known that there does not exist a Diophantine sextuple and that there are only finitely many Diophantine quintuples. On the other hand, there are infinitely many Diophantine m-tuples for m = 2, 3 and 4. In this paper, we derive asymptotic extimates for the numb...
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تاریخ انتشار 2009