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arXiv · 2405.13060

Remark on Pascal's Triangle

Chaim Goodman-Strauss
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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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Chaim Goodman-Strauss. 2024-05-20. Remark on Pascal's Triangle. https://arxiv.org/abs/2405.13060

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