Far Eastern Mathematical Journal

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A multiplicative method of construction of integer Somos-8 and Somos-9 sequences

Monina M.D.

2016, issue 1, P. 62-68

Abstract

The article offers a new method for constructing of integer Somos-8,9 sequences.

Keywords: nonlinear sequences, quadratic recurrence sequences, Weierstrass sigma-function, Somos sequences

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References

[1] M. Ward, «Memoir on elliptic divisibility sequences», Amer. J. Math., 70, 1948, 31–74. [2] M. Somos, Problem 1470, Crux Mathematicorum 15 208, 1989. [3] D. Gale, «Mathematical Entertainments: The Strange and Surprising Saga of the Somos Sequences», Math. Intel., 13, 1991, 40–42. [4] S. Fomin, A. Zelevinsky, «The Laurent Phenomenon», Adv. Appl. Math., 28, 2002, 19–44. [5] A.N. W. Hone, C.S. Swart, «Integrality and the Laurent phenomenon for Somos 4 and Somos 5 sequences», Mathematical Proceedigs of the Cambridge Philosophical Society, 145 (2008), 65–85. [6] A.N.W. Hone, «Elliptic curves and quadratic recurrence sequences», Bull. Lond. Math. Soc., 37, 2005, 161–171. [7] A.N.W. Hone, «Sigma function solution of the initial value problem for Somos-5 sequences», Trans. Amer. Math. Soc., 359, 2007, 5019–5034. [8] V. Bykovskii, «Elliptic systems of sequences and functions», 2015, http://www.skoltech.ru/app/data/uploads/sites/29/2015/02/Skolkovo_Bykovskii.pdf. [9] M.D. Monina, «O celochislennyh posledovatel'nostjah Somos-8 i Somos-9», Dal'nevostochnyj matematicheskij zhurnal, 15:1 (2015), 70–75.

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