Far Eastern Mathematical Journal

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Integer Somos-4 sequence with rational coefficients

Bikovskii V.A.

2018, issue 2, P. 147-149

Abstract

The paper presents a new example of the integer Somos-4 sequence with rational coefficients.

Keywords: quadratic recurrent sequences, Somos sequences, elliptic functions

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References

[1] M. Somos, “Problem 1470”, Crux Mathematicorum, 15, (1989), 208. [2] D. Gale, “The strange and surprising saga of the Somos sequences”, Mathematical Intelligencer, 13:1, (1991), 40–42. [3] S. Fomin, A. Zelevinsky, “The Laurent phenomenon”, Adv. Appl. Math., 28, (2002), 119–144. [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, “CHetyr?khparametricheskoye semeystvo tselochislennykh posledovatel’nostey Somos-4”, Dal’nevost. matem. zhurn., 18:1, (2018), 85–89. [6] V.A. Bykovskiy, M.D. Monina, “TSelochislennyye posledovatel’nosti Somos-4”, Doklady akademii nauk, 418:5, (2018). [7] Hone A.N.W., “Sigma function solution of the initial value problem for Somos 5 sequences”, ath. Soc., 2006, arXiv: math/0501554.

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