Geodesic
Sequences of binomial coefficients modulo prime
Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 84 (2023), pp. 14-22

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The behavior of infinite sequences of binomial coefficients $\begin{pmatrix} x\\ y\end{pmatrix}\mod p$, $x=0,1,2,\dots$( $p$ is a prime number) is considered. In the search of regularities, preliminary mathematical experiments are carried out using Wolfram Mathematica. The periodicity of these sequences is proved and the length of the period is determined as $p$ to the power of l$\lfloor \log_p(y)\rfloor+1$.
Keywords: experimental mathematics, periods, Mathematica system.
Mots-clés : sequences of binomial coefficients, congruences 
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     author = {V. M. Zyuz'kov},
     title = {Sequences of binomial coefficients modulo prime},
     journal = {Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika},
     pages = {14--22},
     publisher = {mathdoc},
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     url = {http://geodesic.mathdoc.fr/item/VTGU_2023_84_a1/}
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V. M. Zyuz'kov. Sequences of binomial coefficients modulo prime. Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 84 (2023), pp. 14-22. http://geodesic.mathdoc.fr/item/VTGU_2023_84_a1/