PPT Slide

Theorem 1

Given an elliptic curve E with point P = (0,0,1) and

gcd(a3,a4) = 1, then for all k ɭ

• gcd(Xk,Yk) = Zk-1

• Xk = -Zk+1Zk-1

• Zk+2Zk-2 = Zk+1Zk-1Z22 - Z1Z3Zk2

Definition

An elliptic divisibility sequence is a sequence of integers {h} which is a particular solution of

hm+nhm-n = hm+1hm-1hn2 - hn+1hn-1hm2

and such that hn|hm whenever n|m.

It follows that the Zk form an elliptic divisibility sequence.

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