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Elliptic divisibility sequence
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<p>In mathematics, an elliptic divisibility sequence (EDS) is a <a href="/facts/Integer_sequence/4l3pev7C">sequence of integers</a> satisfying a nonlinear recursion relation arising from <a href="/facts/Division_polynomial/4zTV83ED">division polynomials</a> on <a href="/facts/Elliptic_curve/60jvaHSA">elliptic curves</a>. EDS were first defined, and their arithmetic properties studied, by <a href="/facts/Morgan_Ward/WJES5gC7">Morgan Ward</a> 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 <a href="/facts/Logic/8JnpJLtt">logic</a> and <a href="/facts/Cryptography/e94PEVau">cryptography</a>. </p>