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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2409.14375 |
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| _version_ | 1866909322133372928 |
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| author | Simhi, Omer |
| author_facet | Simhi, Omer |
| contents | Strömbergsson and Venkatesh proved that a system of homogeneous linear congruence modulo prime has a positive probability to have a short non-trivial solution. We extend this result and show that the same holds for square-free moduli. In the case of 2-variables single linear congruence, we show that there is a positive probability to have a short solution for all integer moduli as well as positive probability for having short non-trivial solutions which are primitive in a suitable sense. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_14375 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Short Solutions To Homogenous Linear congruences Simhi, Omer Number Theory Strömbergsson and Venkatesh proved that a system of homogeneous linear congruence modulo prime has a positive probability to have a short non-trivial solution. We extend this result and show that the same holds for square-free moduli. In the case of 2-variables single linear congruence, we show that there is a positive probability to have a short solution for all integer moduli as well as positive probability for having short non-trivial solutions which are primitive in a suitable sense. |
| title | Short Solutions To Homogenous Linear congruences |
| topic | Number Theory |
| url | https://arxiv.org/abs/2409.14375 |