A FAMILY OF INTEGER SOMOS SEQUENCES

Gezer B., Capa B., Bizim O.

MATHEMATICAL REPORTS, cilt.18, ss.417-435, 2016 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 18
  • Basım Tarihi: 2016
  • Dergi Adı: MATHEMATICAL REPORTS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.417-435
  • Anahtar Kelimeler: Somos sequences, elliptic curves, torsion points, ELLIPTIC DIVISIBILITY SEQUENCES, LUCAS SEQUENCES, LAURENT PHENOMENON, PERFECT POWERS, SQUARES, CUBES, FIBONACCI, TORSION, CURVES
  • Bursa Uludağ Üniversitesi Adresli: Evet

Özet

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.