On a question of Mordell. [PDF]
Proc Natl Acad Sci U S A, 2021 Booker AR, Sutherland AV.
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От алгебраических методов Диофанта - Ферма - Эйлера к арифметике алгебраических кривых: из истории диофантовых уравнений после Эйлера [PDF]
Talking about the Diophantine analysis’ history, namely, the problem of rational solutions of Diophantine equations, we should note the longevity of the algebraic approach, which goes back to Diophantus’ “Arithmetica”.
Беляев А.А. +1 more
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On generating functions in additive number theory, II: lower-order terms and applications to PDEs. [PDF]
Math Ann, 2021 Brandes J +4 more
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The Mordell-Schinzel conjecture for cubic diophantine equations
Building on the works of Mordell (1952) and Schinzel (2015), we prove that cubic diophantine equations $xyz=G(x,y)$ have infinitely many solutions.
Kollár, János, Li, Jennifer
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A Family of Cubic Diophantine Equations and 4-Chains
, 2017 In a simple integer chain, if $u_{i-1}$, $u_i$, and $u_{i+1}$ are three consecutive terms of the chain, and the pair $(u_{i-1}, u_i)$ has a certain property, then the next pair $(u_i, u_{i+1})$ also has the same property. We extend the idea of a simple chain to an $n$-chain in which $n$ is a positive integer and if a pair $(u_{i-1}, u_{i})$ has a ...
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Asymptotically counting points of bounded height [PDF]
, 2008 Widmer, Martin Lucien
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The Classification of Monogenic Quartic Orders via Diophantine Equations [PDF]
In this study, we will focus on classifying quartic monogenic orders based ontwo algebraic relations. First, we introduce index forms and study the connection between the solution set of particular index form equations and the monogenizations type of ...
Shumaker, Jaxon
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On Bounds and Diophantine Properties of Elliptic Curves [PDF]
Mordell equations are celebrated equations within number theory and are named after Louis Mordell, an American-born British mathematician, known for his pioneering research in number theory. In this paper, we discover all Mordell equations of the form $y^
Anand, Navvye
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Considering The Satisfiability of Cubic Diophantine Equations
Our contribution is a bounded cubic compilation theorem. For each fixed resource parameter $k$, syntactic proof checking at resource level $k$ is faithfully represented by a finite bounded-domain system of cubic polynomial equations. Every emitted equation has degree at most 3.
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Perspectives on mathematics competitions and their relationship with mathematics education. [PDF]
ZDM, 2022 de Losada MF, Taylor PJ.
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