Elliptic Divisibility Sequence
In mathematics, an elliptic divisibility sequence (EDS) is a sequence of integers satisfying a nonlinear recursion relation arising from division polynomials on elliptic curves. EDS were first defined, and their arithmetic properties studied, by Morgan Ward in the 1940s. They attracted only sporadic attention until around 2000, when EDS were taken up as a class of nonlinear recurrences that are more amenable to analysis than most such sequences. This tractability is due primarily to the close connection between EDS and elliptic curves. In addition to the intrinsic interest that EDS have within number theory, EDS have applications to other areas of mathematics including logic and cryptography.
Read more about Elliptic Divisibility Sequence: Definition, Divisibility Property, General Recursion, Nonsingular EDS, Examples, Periodicity of EDS, Elliptic Curves and Points Associated To EDS, Growth of EDS, Primes and Primitive Divisors in EDS, EDS Over Finite Fields, Applications of EDS
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... He uses the existence of primitive divisors in EDS on elliptic curves of rank one to prove the undecidability of Hilbert's tenth problem over certain rings of integers ... Katherine Stange has applied EDS and their higher rank generalizations called elliptic nets to cryptography ... value of the Weil and Tate pairings on elliptic curves over finite fields ...
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