Simple proof of the integrality of the Somos-5 sequence

Abstract

In this paper, a simple proof that shows that the Somos-5 sequence produces only natural numbers is given. We also give simple proof that each $a_n$ in the Somos-5 sequence is relatively prime to its four predecessors. The manner in which the integrality is proven is taken from the 1992 proof for the integrality of the Somos-4 sequence by Janice. L. Malouf. The manner in which it is proven that each $a_n$ is relatively prime to its four predecessors is taken from a paper from Michael J. Crabb, who proved that each $a_n$ in the Somos-5 sequence is relatively prime to its two predecessors.