Zobrazeno 1 - 10
of 326
pro vyhledávání: '"DUJELLA, ANDREJ"'
A set of $m$ distinct nonzero rationals $\{a_1, a_2,\ldots, a_m\}$ such that $a_i a_j+1$ is a perfect square for all $1\le i
Externí odkaz:
http://arxiv.org/abs/2403.17959
Let $q$ be an integer. A $D(q)$-$m$-tuple is a set of $m$ distinct positive integers ${a_1, a_2, . . . , a_m}$ such that $a_ia_j + q$ is a perfect square for all $1 \leq i < j \leq m$. By counting integer solutions $x \in [1, b]$ of congruences $x^2
Externí odkaz:
http://arxiv.org/abs/2304.01775
Autor:
Dujella, Andrej, Peral, Juan Carlos
Publikováno v:
Rad Hrvat. Akad. Znan. Umjet. Mat. Znan. 28 (2024), 185-192
In this note we present the main details of the construction of an elliptic curve over $\mathbb{Q}(u)$ with torsion $\mathbb{Z}/4\mathbb{Z}$ and rank 6. Previously only rank 5 examples for such curves were known.
Comment: 7 pages, to appear in R
Comment: 7 pages, to appear in R
Externí odkaz:
http://arxiv.org/abs/2207.08206
Publikováno v:
Acta Arithmetica 208 (2023) no.3, 199-213
For $m \geq 3$, we define the $m$th order pyramidal number by \[ \mathrm{Pyr}_m(x) = \frac{1}{6} x(x+1)((m-2)x+5-m). \] In a previous paper, written by the first-, second-, and fourth-named authors, all solutions to the equation $\mathrm{Pyr}_m(x) =
Externí odkaz:
http://arxiv.org/abs/2112.03782
Autor:
Dujella, Andrej, Soydan, Gökhan
Publikováno v:
Proc. Japan Acad. Ser. A Math. Sci. 98 (2022), 1-6
In this paper, we consider elliptic curves induced by rational Diophantine quadruples, i.e. sets of four nonzero rationals such that the product of any two of them plus 1 is a perfect square. We show that for each of the groups $\mathbb{Z}/2\mathbb{Z
Externí odkaz:
http://arxiv.org/abs/2105.07293
Publikováno v:
Rev. R. Acad. Cienc. Exactas Fis. Nat. Ser. A Math. RACSAM 115 (2021), Article 169
In this paper, we present details of seven elliptic curves over $\mathbb{Q}(u)$ with rank $2$ and torsion group $\mathbb{Z}/ 8\mathbb{Z}$ and five curves over $\mathbb{Q}(u)$ with rank $2$ and torsion group $\mathbb{Z}/ 2\mathbb{Z} \times \mathbb{Z}/
Externí odkaz:
http://arxiv.org/abs/2105.06215
Publikováno v:
Rev. R. Acad. Cienc. Exactas Fis. Nat. Ser. A Math. RACSAM 115 (2021), Article 172
For an integer n, a set of m distinct nonzero integers {a_1,a_2,...,a_m} such that a_i a_j+n is a perfect square for all 0
Externí odkaz:
http://arxiv.org/abs/2011.01684
Autor:
Dujella, Andrej, Mikić, Miljen
Publikováno v:
Rad Hrvat. Akad. Znan. Umjet. Mat. Znan. 24 (2020), 29-37
Rational Diophantine triples, i.e. rationals a,b,c with the property that ab+1, ac+1, bc+1 are perfect squares, are often used in construction of elliptic curves with high rank. In this paper, we consider the opposite problem and ask how small can be
Externí odkaz:
http://arxiv.org/abs/2005.11666
Autor:
Dujella, Andrej, Peral, Juan Carlos
Publikováno v:
Glas. Mat. Ser. III 55 (2020), 237-252
A rational Diophantine triple is a set of three nonzero rational a,b,c with the property that ab+1, ac+1, bc+1 are perfect squares. We say that the elliptic curve y^2 = (ax+1)(bx+1)(cx+1) is induced by the triple {a,b,c}. In this paper, we describe a
Externí odkaz:
http://arxiv.org/abs/2005.10706
Autor:
Dujella, Andrej, Petričević, Vinko
Publikováno v:
Rev. R. Acad. Cienc. Exactas Fis. Nat. Ser. A Math. RACSAM 114 (2020), Article 189
For a nonzero integer n, a set of m distinct nonzero integers {a_1,a_2,...,a_m} such that a_i a_j + n is a perfect square for all 1 <= i < j <= m, is called a D(n)-m-tuple. In this paper, by using properties of so-called regular Diophantine m-tuples
Externí odkaz:
http://arxiv.org/abs/2001.10702