Results 1 to 10 of about 1,054 (55)
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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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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Upper bounds for the number of solutions to quartic Thue equations [PDF]
, 2011 We will give upper bounds for the number of integral solutions to quartic Thue equations. Our main tool here is a logarithmic curve (x,y) that allows us to use the theory of linear forms in logarithms.
Akhtari, S.
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Extremal families of cubic Thue equations [PDF]
, 2014 We exactly determine the integral solutions to a previously untreated infinite family of cubic Thue equations of the form $F(x,y)=1$ with at least $5$ such solutions.
Bennett, Michael A., Ghadermarzi, Amir
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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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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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On certain diophantine equations of diagonal type
, 2013 In this note we consider Diophantine equations of the form \begin{equation*} a(x^p-y^q) = b(z^r-w^s), \quad \mbox{where}\quad \frac{1}{p}+\frac{1}{q}+\frac{1}{r}+\frac{1}{s}=1, \end{equation*} with even positive integers $p,q,r,s$.
Bremner, Andrew, Ulas, Maciej
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A note on Diophantine systems involving three symmetric polynomials
, 2013 Let $\bar{X}_{n}=(x_{1},\ldots,x_{n})$ and $\sigma_{i}(\bar{X}_{n})=\sum x_{k_{1}}\ldots x_{k_{i}}$ be $i$-th elementary symmetric polynomial. In this note we prove that there are infinitely many triples of integers $a, b, c$ such that for each $1\leq i ...
Ulas, Maciej
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