On Periodicity of the Somos Sequences Modulo $m$
A. V. Ustinov ab email email 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.
Received: 28.07.2023Revised: 20.09.2023
Citation:
A. V. Ustinov, “On Periodicity of the Somos Sequences Modulo $m$ ”, Mat. Zametki , 115 :3 (2024), 439–449 ; Math. Notes , 115 :3 (2024), 405–413
Linking options:
https://www.mathnet.ru/eng/mzm14120 https://doi.org/10.4213/mzm14120 https://www.mathnet.ru/eng/mzm/v115/i3/p439