A FAMILY OF INTEGER SOMOS SEQUENCES


Gezer B. , Capa B., Bizim O.

MATHEMATICAL REPORTS, vol.18, pp.417-435, 2016 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 18
  • Publication Date: 2016
  • Title of Journal : MATHEMATICAL REPORTS
  • Page Numbers: pp.417-435

Abstract

Somos sequences are sequences of rational numbers defined by a bilinear recurrence relation. Remarkably, although the recurrences describing the Somos sequences are rational, some Somos sequences turn out to have only integer terms. In this paper, a family of Somos 4 sequences is given and it is proved that all Somos 4 sequences associated to Tate normal forms with h(-1) - +/- 1 consist entirely of integers for n >= 0. It is also shown that there are infinitely many squares and infinitely many cubes in Somos 4 sequences associated to Tate normal forms.