Výsledky vyhledávání - "Tadic, Petra"

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Autor: Dujella, Andrej, Gusić, Ivica, Petričević, Vinko, Tadić, Petra

Publikováno v: Glas. Mat. Ser. III 53 (2018), 33-42

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.
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Externí odkaz: http://arxiv.org/abs/1802.00291

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Triples which are $D(n)$-sets for several $n$'s

Autor: Adžaga, Nikola, Dujella, Andrej, Kreso, Dijana, Tadić, Petra

Publikováno v: J. Number Theory 184 (2018), 330-341

For a nonzero integer $n$, a set of distinct nonzero integers $\{a_1,a_2,\ldots,a_m\}$ such that $a_ia_j+n$ is a perfect square for all $1\leq i

Externí odkaz: http://arxiv.org/abs/1703.10659

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The rank and generators of Kihara's elliptic curve with torsion $\mathbb{Z}/4\mathbb{Z}$ over $\mathbb{Q}(t)$

Autor: Dujella, Andrej, Gusić, Ivica, Tadić, Petra

Publikováno v: Proc. Japan Acad. Ser. A Math. Sci. 91 (2015), 105-109

For the elliptic curve $E$ over $\mathbb{Q}(t)$ found by Kihara, with torsion group $\mathbb{Z}/4\mathbb{Z}$ and rank $\geq 5$, which is the current record for the rank of such curves, by using a suitable injective specialization, we determine exactl

Externí odkaz: http://arxiv.org/abs/1410.6919

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Injectivity of the specialization homomorphism of elliptic curves

Autor: Gusić, Ivica, Tadić, Petra

Let $E:y^2=x^3+Ax^2+Bx+C$ be a nonconstant elliptic curve over $\mathbb{Q}(t)$ with at least one nontrivial $\mathbb{Q}(t)$-rational $2$-torsion point. We describe a method for finding $t_0\in\mathbb Q$ for which the corresponding specialization homo

Externí odkaz: http://arxiv.org/abs/1409.7189

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Injectivity of the specialization homomorphism of elliptic curves

Autor: Gusic, Ivica, Tadic, Petra

Let $E:y^2=(x-e_1)(x-e_2)(x-e_3)$ be a nonconstant elliptic curve over $\mathbb{Q}(t)$, where $e_j\in \mathbb{Z}[t]$. We describe a method for finding a specialization $t\mapsto t_0\in\mathbb{Q}$ such that the specialization homomorphism is injective

Externí odkaz: http://arxiv.org/abs/1211.3851

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