Remark on Pascal's Triangle

2024/05/20 by Chaim Goodman-Strauss, Goodman-Strauss, Chaim
Mathematics · #11A99 #FOS: Mathematics #History and Overview (math.HO) #History and Theory of Mathematics

paper · pdf · doi:10.48550/arxiv.2405.13060

openalex publication_date 2024/05/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Through a series of elementary exercises, we explain the fractal structure of Pascal's triangle when written modulo p using an 1852 theorem due to Kummer: A prime p divides \dfrac n!i!j! if and only if there is a carry in the addition i+j=n when written in base p.

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