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Integer Somos-4 sequence with rational coefficients. (Russian. English summary) Zbl 1411.11010

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

MSC:

11B37 Recurrences
33E05 Elliptic functions and integrals
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Full Text: MNR

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 · Zbl 1012.05012
[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 · Zbl 1165.11018
[5] M. D. Monina, “Chetyrëkhparametricheskoe semeistvo tselochislennykh posledovatelnostei Somos-4”, Dalnevost. matem. zhurn., 18:1 (2018), 85–89
[6] V. A. Bykovskii, M. D. Monina, “Tselochislennye posledovatelnosti Somos-4”, Doklady akademii nauk, 418:5 (2018) · Zbl 1464.11020
[7] Hone A. N. W., “Sigma function solution of the initial value problem for Somos 5 sequences”, Trans. Amer. Math. Soc., 2006, arXiv: · Zbl 1162.11011
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