Elliptic Nets and Points on Elliptic Curves
نویسندگان
چکیده
(2) hn divides hm whenever n divides m. They have attracted number theoretical and combinatorial interest as some of the simplest nonlinear recurrence sequences (see [3] for references), but for us their interest lives in the underlying geometry: Ward demonstrates that an elliptic divisibility sequence arises from any choice of elliptic curve over Q and rational point on that curve. Theorem 1 (M. Ward, 1948, [11]). Suppose E is an elliptic curve defined over Q, σ : C → C is its Weierstrass sigma function, and u ∈ C corresponds to a rational point on E. Then there exists an integer k such that the sequence
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