A simplified proof of Ward's formula for elliptic sequences

A. V. Ustinov<sup>ab

a</sup> Pacific National University, Khabarovsk
^b Khabarovsk Division of the Institute for Applied Mathematics, Far Eastern Branch, Russian Academy of Sciences

Abstract: 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 in the 1948. In particular he has proven an explicit formula for the general term of the sequence in terms of the Weierstrass sigma function. In the present paper we give a simplified proof of Ward's formula.

Key words: elliptic divisibility sequence, elliptic curves, Weierstrass elliptic functions.

UDC: 517.583+512.742.72

MSC: 33E05

Received: 21.04.2019