Results 1 to 10 of about 59 (48)
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
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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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Investigations into light-front interactions for massless fields (I): non-constructibility of higher spin quartic amplitudes [PDF]
Journal of High Energy Physics, 2016 A bstractThe dynamical commutators of the light-front Poincaré algebra yield first order differential equations in the p+ momenta for the interaction vertex operators.
A. Bengtsson
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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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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
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Arithmetic upon an algebraic surface
, 1945 The title of my lecture is, I am afraid, probably misleading and certainly too ambitious. For, on the one hand, the connection between arithmetic and geometry suggested by it is not the modern development in divisors theory, but an application of ...
B. Segre
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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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his article introduces a novel generalized scaling approximation method for efficiently finding rational approximations to cubic and quartic Diophantine equations. While Diophantine equations have fascinated mathematicians due to their simple forms yet extremely challenging integer solutions, finding exact solutions remains computationally infeasible ...
openaire +2 more sources
HERON QUADRILATERALS VIA ELLIPTIC CURVES. [PDF]
Rocky Mt J Math, 2017 Izadi F, Khoshnam F, Moody D.
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ON THE USE OF ABSTRACT ALGEBRA AS A METHOD FOR OBTAINING RESULTS INVOLVING RATIONAL INTEGERS ONLY AND THE REVERSE OF THIS PROCEDURE. [PDF]
Proc Natl Acad Sci U S A, 1960 Vandiver HS.
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