Results 21 to 30 of about 202 (150)
On units of certain cubic fields and the Diophantine equation 𝑥³+𝑦³+𝑧³=3 [PDF]
, 1984 The Diophantine equation x 3 + y 3 + z 3 = 3 {x^3} + {y^
Manny Scarowsky
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Some Diophantine Problems [PDF]
, 1944 This thesis is concerned with the problem of exhibiting all the rational integer solutions satisfying certain diophantine equations. The thesis consists of two sections.
Rosenthall, Edward
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An Analysis on the Ternary Cubic Diophantine Equation
International Journal for Research in Applied Science and Engineering Technology, 2023 Abstract: In this article, we concentrate on identifying all the non-zero, infinitely many integral solutions to the ternary cubic ...
openaire +1 more source
A repulsion motif in Diophantine equations [PDF]
, 2011 Problems related to the existence of integral and rational points on cubic curves date back at least to Diophantus. A significant step in the modern theory of these equations was made by Siegel, who proved that a nonsingular plane cubic equation has only
Ward, T. +5 more
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Diophantine problems over global fields and a conjecture of Artin over function fields [PDF]
, 2023 This thesis considers three diophantine problems over different global fields and Artin's primitive root conjecture over function fields. In the first chapter, which is a joint project with Christian Bernert, the main result is that every cubic form over
Hochfilzer, Leonhard
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An algorithm for solving a certain class of Diophantine equations. I [PDF]
, 1982 A class of Diophantine equations is defined and an algorithm for solving each equation in this class is developed. The methods consist of techniques for the computation of an upper bound for the absolute value of each solution. The computability of these
David Lee Hilliker
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Rational solutions of pairs of diagonal equations, one cubic and one quadratic [PDF]
, 2014 We obtain an essentially optimal estimate for the moment of order 32/3 of the exponential sum having argument $\alpha x^3+\beta x^2$. Subject to modest local solubility hypotheses, we thereby establish that pairs of diagonal Diophantine equations, one ...
Wooley, Trevor D. +2 more
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Multiplicatively dependent integer vectors on a hyperplane
Journal of the London Mathematical Society, Volume 114, Issue 1, July 2026.Abstract We establish several asymptotic formulae and upper bounds for the count of multiplicatively dependent integer vectors that lie on a fixed affine hyperplane and have bounded height. This work constitutes a direct extension of the results obtained by Pappalardi, Sha, Shparlinski, and Stewart.
Muhammad Afifurrahman +2 more
wiley +1 more source
Algorithms for Hermite and Smith normal matrices and linear Diophantine equations [PDF]
, 1971 New algorithms for constructing the Hermite normal form (triangular) and Smith normal form (diagonal) of an integer matrix are presented. A new algorithm for determining the set of solutions to a system of linear diophantine equations is presented.
Gordon H. Bradley
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Solving the n $n$‐Player Tullock Contest
Journal of Public Economic Theory, Volume 28, Issue 2, April 2026.ABSTRACT The n $n$‐player Tullock contest with complete information is known to admit explicit solutions in special cases, such as (i) homogeneous valuations, (ii) constant returns, and (iii) two contestants. But can the model be solved more generally?
Christian Ewerhart
wiley +1 more source