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JOURNALS // Matematicheskie Zametki // Archive
Mat. Zametki, 2024 Volume 115, Issue 3, Pages 439–449 (Mi mzm14120)
On Periodicity of the Somos Sequences Modulo $m$

A. V. Ustinovab

a Khabarovsk Division of the Institute for Applied Mathematics, Far Eastern Branch, Russian Academy of Sciences
b HSE University, Moscow

Abstract: We prove the periodicity of finite rank Somos sequences modulo $m$. As an application, we prove the periodicity of the Somos-$(6)(\mathrm{mod}\ m)$ sequence.

Keywords: Somos sequence, division polynomial, elliptic-curve cryptography.

UDC: 511.21

MSC: 11B50

Received: 28.07.2023
Revised: 20.09.2023

DOI: 10.4213/mzm14120


 English version: Mathematical Notes, 2024, 115:3, 405–413

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© Steklov Math. Inst. of RAS, 2025