Results 1 to 10 of about 56 (52)
Perspectives on mathematics competitions and their relationship with mathematics education. [PDF]
ZDM, 2022 de Losada MF, Taylor PJ.
europepmc +1 more source
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 ...
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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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Cubic and Quartic Diophantine Equations [PDF]
Springer Undergraduate Mathematics Series, 2020 In Chapters 3 and 4 we were concerned with quadratic equations in two variables, but were only allowing ourselves integer solutions. An equation involving polynomials together with the constraint that we are only interested in integer solutions is called a Diophantine equation. In this sense we have been considering ‘quadratic Diophantine equations’.
Menny Aka +2 more
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Some of the next articles are maybe not open access.
International Journal of Research and Scientific Innovation
We establish the complete non-existence of integer solutions to the Diophantine equation y3 + xy = x4 +4, thereby resolving an open problem in the classification of quartic- cubic Diophantine equations. Our proof employs a novel synthesis of classical techniques: we utilize Sophie Germain’s identity for the factorization of quartic forms, develop a com-
Aditya Patil, Abhay Nenavath
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We establish the complete non-existence of integer solutions to the Diophantine equation y3 + xy = x4 +4, thereby resolving an open problem in the classification of quartic- cubic Diophantine equations. Our proof employs a novel synthesis of classical techniques: we utilize Sophie Germain’s identity for the factorization of quartic forms, develop a com-
Aditya Patil, Abhay Nenavath
openaire +2 more sources
Diophantine problems related to cyclic cubic and quartic fields
Journal of Number Theory, 2022Maciej Ulas, Szabolcs Tengely
exaly