Remark on Pascal's Triangle
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909210926645248 |
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| author | Goodman-Strauss, Chaim |
| author_facet | Goodman-Strauss, Chaim |
| contents | 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 $p$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_13060 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Remark on Pascal's Triangle Goodman-Strauss, Chaim History and Overview 11A99 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 $p$. |
| title | Remark on Pascal's Triangle |
| topic | History and Overview 11A99 |
| url | https://arxiv.org/abs/2405.13060 |