Zobrazeno 1 - 10
of 49
pro vyhledávání: '"Adžaga, Nikola"'
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:
Adžaga, Nikola, Keller, Timo, Michaud-Jacobs, Philippe, Najman, Filip, Ozman, Ekin, Vukorepa, Borna
In this paper we improve on existing methods to compute quadratic points on modular curves and apply them to successfully find all the quadratic points on all modular curves $X_0(N)$ of genus up to $8$, and genus up to $10$ with $N$ prime, for which
Externí odkaz:
http://arxiv.org/abs/2303.12566
We complete the computation of all $\mathbb{Q}$-rational points on all the $64$ maximal Atkin-Lehner quotients $X_0(N)^*$ such that the quotient is hyperelliptic. To achieve this, we use a combination of various methods, namely the classical Chabauty
Externí odkaz:
http://arxiv.org/abs/2203.05541
Autor:
Adžaga, Nikola, Arul, Vishal, Beneish, Lea, Chen, Mingjie, Chidambaram, Shiva, Keller, Timo, Wen, Boya
We use the method of quadratic Chabauty on the quotients $X_0^+(N)$ of modular curves $X_0(N)$ by their Fricke involutions to provably compute all the rational points of these curves for prime levels $N$ of genus four, five, and six. We find that the
Externí odkaz:
http://arxiv.org/abs/2105.04811
Let $k$ be a positive integer. In this paper, we prove that if $\{k,k+1,c,d\}$ is a $D(-k)$-quadruple with $c>1$, then $d=1$.
Comment: 15 pages
Comment: 15 pages
Externí odkaz:
http://arxiv.org/abs/2001.04160
A Diophantine $m$-tuple is a set of $m$ distinct integers such that the product of any two distinct elements plus one is a perfect square. In this paper we study the extensibility of a Diophantine triple $\{k-1, k+1, 16k^3-4k\}$ in Gaussian integers
Externí odkaz:
http://arxiv.org/abs/1905.09332
Autor:
Adžaga, Nikola
A Diophantine $m$-tuple is a set of $m$ distinct integers such that the product of any two distinct elements plus one is a perfect square. It was recently proven that there is no Diophantine quintuple in positive integers. We study the same problem i
Externí odkaz:
http://arxiv.org/abs/1807.01896
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
Autor:
Adžaga, Nikola, Filipin, Alan
Publikováno v:
Moscow Mathematical Journal 17, no. 2, 165-174 (2017)
Let $n$ be a nonzero integer. A set of $m$ positive integers is called a $D(n)$-$m$-tuple if the product of any two of its distinct elements increased by $n$ is a perfect square. Let $k$ be a positive integer. By elementary means, we show that the $D
Externí odkaz:
http://arxiv.org/abs/1610.04415
Publikováno v:
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, Vol 29, Iss 2, Pp 5-24 (2021)
The aim of this paper is to consider the extensibility of the Diophantine triple {2, b, c}, where 2 < b < c, and to prove that such a set cannot be extended to an irregular Diophantine quadruple. We succeed in that for some families of c’s (dependi
Externí odkaz:
https://doaj.org/article/817b6aedf8c04f339b41d76c7f123e20
