Elliptic Divisibility Sequence - Definition

Definition

A (nondegenerate) elliptic divisibility sequence (EDS) is a sequence of integers (Wn)n ≥ 1 defined recursively by four initial values W1, W2, W3, W4, with W1W2W3 ≠ 0 and with subsequent values determined by the formulas

 \begin{align} W_{2n+1}W_1^3 &= W_{n+2}W_n^3 - W_{n+1}^3W_{n-1},\qquad n \ge 2, \\ W_{2n}W_2W_1^2 &= W_{n+2}W_n W_{n-1}^2 - W_n W_{n-2}W_{n+1}^2,\qquad n\ge 3,\\ \end{align}

It can be shown that if W1 divides each of W2, W3, W4 and if further W2 divides W4, then every term Wn in the sequence is an integer.

Read more about this topic:  Elliptic Divisibility Sequence

Famous quotes containing the word definition:

    Scientific method is the way to truth, but it affords, even in
    principle, no unique definition of truth. Any so-called pragmatic
    definition of truth is doomed to failure equally.
    Willard Van Orman Quine (b. 1908)

    According to our social pyramid, all men who feel displaced racially, culturally, and/or because of economic hardships will turn on those whom they feel they can order and humiliate, usually women, children, and animals—just as they have been ordered and humiliated by those privileged few who are in power. However, this definition does not explain why there are privileged men who behave this way toward women.
    Ana Castillo (b. 1953)

    No man, not even a doctor, ever gives any other definition of what a nurse should be than this—”devoted and obedient.” This definition would do just as well for a porter. It might even do for a horse. It would not do for a policeman.
    Florence Nightingale (1820–1910)