A family of integer Somos sequences

Please use this identifier to cite or link to this item: http://hdl.handle.net/11452/32978

Title:	A family of integer Somos sequences
Authors:	Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü. Gezer, Betül Çapa, Buse Bizim, Osman AAH-1547-2021 AAH-1468-2021 24485316600 57194222837 9245697900
Keywords:	Mathematics Somos sequences Elliptic curves Torsion points Elliptic divisibility sequences Lucas sequences Laurent phenomenon Perfect powers Squares Cubes Fibonacci Torsion Curves
Issue Date:	2016
Publisher:	Editura Acad Romane
Citation:	Gezer, B. vd. (2016). "A family of integer Somos sequences". Mathematical Reports, 18(3), 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.
URI:	http://hdl.handle.net/11452/32978
ISSN:	1582-3067
Appears in Collections:	Scopus Web of Science

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