A Question of Erdős and Graham on Covering Systems
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866917120426639360 |
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| author | Adenwalla, Sarosh |
| author_facet | Adenwalla, Sarosh |
| contents | Erdős and Graham (Erdős and Graham, 1980) asked if there exists an $n$ such that the divisors of $n$ greater than 1 are the moduli of a distinct covering system with the following property: If there exists an integer which satisfies two congruences in the system, $a\mod d$ and $a'\mod d'$, then $\gcd(d,d')=1$. We show that such an $n$ does not exist. This problem is part of Problem # 204 on the website www.erdosproblems.com, compiled and maintained by Thomas Bloom. We also study when the divisors of $n$ greater than $1$ can form a congruence system satisfying the above condition. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_15170 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Question of Erdős and Graham on Covering Systems Adenwalla, Sarosh Number Theory Combinatorics 11A07 Erdős and Graham (Erdős and Graham, 1980) asked if there exists an $n$ such that the divisors of $n$ greater than 1 are the moduli of a distinct covering system with the following property: If there exists an integer which satisfies two congruences in the system, $a\mod d$ and $a'\mod d'$, then $\gcd(d,d')=1$. We show that such an $n$ does not exist. This problem is part of Problem # 204 on the website www.erdosproblems.com, compiled and maintained by Thomas Bloom. We also study when the divisors of $n$ greater than $1$ can form a congruence system satisfying the above condition. |
| title | A Question of Erdős and Graham on Covering Systems |
| topic | Number Theory Combinatorics 11A07 |
| url | https://arxiv.org/abs/2501.15170 |