Solution to the Erdos problem on distinct residues of factorials
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866910262917857280 |
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| author | Abramov, Vyacheslav M. |
| author_facet | Abramov, Vyacheslav M. |
| contents | Paul Erdos posed the following question: Is there a prime number $p>5$ such that the residues of $2!$, $3!$,\ldots, $(p-1)!$ modulo $p$ all are distinct. In this short note, we give the negative answer on this question in an elementary way. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_26429 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Solution to the Erdos problem on distinct residues of factorials Abramov, Vyacheslav M. Number Theory Combinatorics 11A41, 11A07, 05A10 Paul Erdos posed the following question: Is there a prime number $p>5$ such that the residues of $2!$, $3!$,\ldots, $(p-1)!$ modulo $p$ all are distinct. In this short note, we give the negative answer on this question in an elementary way. |
| title | Solution to the Erdos problem on distinct residues of factorials |
| topic | Number Theory Combinatorics 11A41, 11A07, 05A10 |
| url | https://arxiv.org/abs/2604.26429 |