Results 1 to 10 of about 1,078 (72)
Quartic index form equations and monogenizations of quartic orders [PDF]
Essential Number Theory, 2022 Some upper bounds for the number of monogenizations of quartic orders are established by considering certain classical Diophantine equations, namely index form equations in quartic number fields, and cubic and quartic Thue equations.
S. Akhtari
semanticscholar +1 more source
On a class of quartic Diophantine equations
, 2021 In this paper, by using elliptic curves theory, we study the quartic Diophantine equation (DE) ∑n i=1 aix 4 i = ∑n j=1 ajy 4 j , where ai and n ≥ 3 are fixed arbitrary integers. We try to transform this quartic to a cubic elliptic curve of positive rank.
F. Izadi, M. Baghalaghdam, S. Kosari
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Simplest quartic and simplest sextic Thue equations over imaginary quadratic fields [PDF]
International Journal of Number Theory, 2018 The families of simplest cubic, simplest quartic and simplest sextic fields and the related Thue equations are well known, see G. Lettl, A. Pethő and P. Voutier, Simple families of Thue inequalities, Trans. Amer. Math. Soc.
Istv'an Ga'al +2 more
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Enumerative Galois theory for cubics and quartics [PDF]
, 2020 We show that there are $O_\varepsilon(H^{1.5+\varepsilon})$ monic, cubic polynomials with integer coefficients bounded by $H$ in absolute value whose Galois group is $A_3$.
Chow, Sam, Dietmann, Rainer
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Integral points on a certain family of elliptic curves [PDF]
, 2015 The Thue-Siegel method is used to obtain an upper bound for the number of primitive integral solutions to a family of quartic Thue's inequalities. This will provide an upper bound for the number of integer points on a family of elliptic curves with j ...
Akhtari, Shabnam
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On a class of quartic Diophantine equations of at least five variables
Notes on Number Theory and Discrete Mathematics, 2018 In this paper, elliptic curves theory is used for solving the quartic Diophantine equation X + Y 4 = 2U + ∑n i=1 TiU 4 i , where n ≥ 1, and Ti, are rational numbers.
H. Abdolmalki, F. Izadi
semanticscholar +1 more source
The lost proof of Fermat's last theorem
, 2021 This work contains two papers: the first entitled "Euler's double equations equivalent to Fermat's Last Theorem" presents a marvellous "Eulerian" proof of Fermat's Last Theorem, which could have entered in a not very narrow margin, i.e.
Ossicini, Andrea
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Universal Calabi-Yau Algebra: Classification and Enumeration of Fibrations [PDF]
, 2002 We apply a universal normal Calabi-Yau algebra to the construction and classification of compact complex $n$-dimensional spaces with SU(n) holonomy and their fibrations.
Anselmo, F +3 more
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Finite saturation for unirational varieties [PDF]
, 2017 We import ideas from geometry to settle Sarnak's saturation problem for a large class of algebraic ...
Sofos, Efthymios, Wang, Yuchao
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Constructions of diagonal quartic and sextic surfaces with infinitely many rational points
, 2014 In this note we construct several infinite families of diagonal quartic surfaces \begin{equation*} ax^4+by^4+cz^4+dw^4=0, \end{equation*} where $a,b,c,d\in\Z\setminus\{0\}$ with infinitely many rational points and satisfying the condition $abcd\neq ...
Ajai Choudhry +6 more
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