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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〔Morgan Ward, Memoir on elliptic divisibility sequences, ''Amer. J. Math.'' 70 (1948), 31–74.〕 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. == Definition == A (nondegenerate) ''elliptic divisibility sequence'' (EDS) is a sequence of integers defined recursively by four initial values , , , , with ≠ 0 and with subsequent values determined by the formulas : It can be shown that if divides each of , , and if further divides , then every term in the sequence is an integer. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Elliptic divisibility sequence」の詳細全文を読む スポンサード リンク
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