Results 41 to 50 of about 1,078 (72)
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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-
Abhay Vivek Siddhartha
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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-
Abhay Vivek Siddhartha
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Cubic and Quartic Diophantine Equations
2020In 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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Чебышевский сборник, 2021
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”.
T. Lavrinenko, A. A. Belyaev
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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”.
T. Lavrinenko, A. A. Belyaev
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Algebra and geometry, an introduction to university mathematics
Mathematical Gazette, 2023Algebra and geometry, an introduction to university mathematics (second edition) by Mark V. Lawson, pp. 424, £49.99 (paper), ISBN 978-0-36756-303-5, CRC/Taylor and Francis (2021) This book aims to provide a bridge between school mathematics and ...
N. Lord
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NONLINEAR DIOPHANTINE EQUATIONS IN CRYPTOGRAPHY ALGEBRAIC APPROACHES TO POST-QUANTUM SECURITY
JP Journal of Algebra Number Theory and ApplicationsThis paper investigates nonlinear Diophantine equations as a foundation for post-quantum cryptography. Unlike RSA and ECC, which rely on factorization and discrete logarithms vulnerable to Shor’s algorithm, nonlinear systems with mixed degrees (quadratic,
Mariam Almahdi Mohammed Mulla Mull
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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 ...
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Some quartic curves with no points in any cubic field
, 1986A. Bremner
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On the diophantine equation x 2 + 2 α 5 β 13 γ = y n
, 2008Edray Goins, F. Luca, A. Togbé
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SOME DIOPHANTINE PROBLEMS ARISING FROM THE ISOMORPHISM PROBLEM OF GENERIC POLYNOMIALS
, 2009Akinari Hoshi +1 more
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