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Volume 10, Number 3 (2025)

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RATIONAL POINTS ON ELLIPTIC CURVES; THE ULTIMATE SOLUTION OF THE MILLENIUM PRIZE PROBLEM; BSD-CONJECTURE

Volume 10, Issue 3, June 2025 | PP. 175-183 | PDF (379 K) | Pub. Date: November 29, 2016
DOI: 436 Downloads 10074 Views

Author(s)

Lena J-T Strömberg, previously Department of Solid Mechanics, Royal Institute of Technology (KTH)

Abstract
Rational points on elliptic curves are considered, in the formulation of BSD, and for nonlinear dynamical systems. Method used is the intersection with other curves, for a more general expression of an elliptic curve, known as an extended elliptic curve. It is found that there are elliptic curves with at most 3 rational solutions for certain rational values of parameters, c.f. Theorem 3.

Keywords
Elliptic Curves, Rational numbers, Number Theory, Millennium Prize Problem, ultimate solution, associated ellips, associated hyperbolic, cusp, Nonlinear Dynamics, Phase Portrait, Lorenz equations, aqua plane, Hamiltonian

Cite this paper
Lena J-T Strömberg, RATIONAL POINTS ON ELLIPTIC CURVES; THE ULTIMATE SOLUTION OF THE MILLENIUM PRIZE PROBLEM; BSD-CONJECTURE , SCIREA Journal of Mathematics. Volume 10, Issue 3, June 2025 | PP. 175-183.

References

[ 1 ]	The Birch and Swinnerton-Dyer conjecture, A Wiles, wikipedia, elliptic curves
[ 2 ]	Continuum Mixture theory as an approach to Fluid-Structure Interaction, L Strömberg, IUTAM Symposium on Fluid-Structure Interaction in Ocean Engineering, Hamburg/Germany, July 23-27, 2007 and proc. NSCM 19, Lund, 2006.