2023-06-082023-06-082016Gezer, B. vd. (2016). "A family of integer Somos sequences". Mathematical Reports, 18(3), 417-435.1582-3067http://hdl.handle.net/11452/32978Somos 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.eninfo:eu-repo/semantics/closedAccessMathematicsSomos sequencesElliptic curvesTorsion pointsElliptic divisibility sequencesLucas sequencesLaurent phenomenonPerfect powersSquaresCubesFibonacciTorsionCurvesArticle0003839028000112-s2.0-85019293455417435183MathematicsSymmetry; Discrete Equations; Affine Weyl Groups