Sequences of binomial coefficients modulo prime | Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mekhanika – Tomsk State University Journal of Mathematics and Mechanics. 2023. № 84. DOI: 10.17223/19988621/84/2

Sequences of binomial coefficients modulo prime

We consider the behavior of infinite sequences of binomial coefficients x, y modp, x = 0, 1, 2, ... modulo p. In search of patterns, preliminary mathematical experiments are carried out using Wolfram Mathematica. The periodicity of these sequences is proved and the length of the period kap to the power ⌊log_p(y)⌋ +1 is determined.

Download file

Counter downloads: 6

Keywords

experimental mathematics, sequences of binomial coefficients, periods, congruences, Mathematica system

Authors

Name	Organization	E-mail
Zyuz′kov Valentin M.	Tomsk State University; Tomsk State University of Control Systems and Radioelectronics	vmz@math.tsu.ru

Всего: 1

References

Wolfram Mathematica. URL: http://www.wolfram.com/mathematica.

Weisstein E.W. Experimental Mathematics // Wolfram MathWorld. URL: https://mathworld.wolfram.com/ExperimentalMathematics.html.

Зюзьков В.М. Эксперименты в теории чисел. Томск: Изд-во НТЛ, 2019. 348 с.

Грэхем Р., Кнут Д., Поташник О. Конкретная математика. Основание информатики. М.: Мир; БИНОМ. Лаборатория знаний, 2006. 703 с.

Табачников С.Л., Фукс Д.Б. Математический дивертисмент: 30 лекций по классической математике. М.: МЦНМО, 2011. 512 с.