On the Integrality of Somos 4 Sequences

In this paper, it is shown that if (hn) is a Somos 4 sequence associated to an elliptic curve then each hn can be expressed as elements of the ring R = ？[a1, a2, a3, a4, x, y, h–1±1, h0]. In particular, if h –1 = ±1, then the Somos 4 sequence consist entirely of integers for n ≥ 0. Also the general term of the Somos 4 sequence is given which satisfies a binary recurrence relation