Far Eastern Mathematical Journal

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Four-parameter family of integer sequences Somos-4

Monina M.D.

2018, issue 1, P. 85-89

Abstract

A four-parameter family of integer Somos-4 sequences is constructed, a special case of which is the three-parameter family Somos-4.

Keywords: Somos sequences, elliptic functions, addition theorems

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References

[1] Fomin S., Zelevinsky A., “The Laurent phenomenon”, Adv. Appl. Math., 28, (2002), 119–144. [2] Somos M., Somos Polynomials, http://somos.crg4.com/somospol.html. [3] Somos M., “Problem 1470”, Crux Mathematicorum, 15, (1989), 208. [4] 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. [5] M.D. Monina, “O celochislennyh posledovatel'nostjah Somos-8 i Somos-9”, Dal'nevostochnyj matematicheskij zhurnal, 15:1, (2015), 70–75. [6] A.N.W. Hone, “Elliptic curves and quadratic recurrence sequences”, Bulletin of the London Mathematical Society, 37, 2005, 161–171. [7] R. Shipsey, Elliptic Divisibility Sequences, PhD Thesis, Goldsmith’s University of London, 2000. [8] C. Swart, Elliptic curves and related sequences, PhD Thesis, Royal Holloway and Bedford New College, University of London, 2003.

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