More on consecutive multiplicatively dependent triples of integers
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913581737443328 |
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| author | Bennett, Michael A. Pink, István Vukusic, Ingrid |
| author_facet | Bennett, Michael A. Pink, István Vukusic, Ingrid |
| contents | In this paper, we extend recent work of the third author and Ziegler on triples of integers $(a,b,c)$, with the property that each of $(a,b,c)$, $(a+1,b+1,c+1)$ and $(a+2,b+2,c+2)$ is multiplicatively dependent, completely classifying such triples in case $a=2$. Our techniques include a variety of elementary arguments together with more involved machinery from Diophantine approximation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_12009 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | More on consecutive multiplicatively dependent triples of integers Bennett, Michael A. Pink, István Vukusic, Ingrid Number Theory 11N25, 11D61, 11J86 In this paper, we extend recent work of the third author and Ziegler on triples of integers $(a,b,c)$, with the property that each of $(a,b,c)$, $(a+1,b+1,c+1)$ and $(a+2,b+2,c+2)$ is multiplicatively dependent, completely classifying such triples in case $a=2$. Our techniques include a variety of elementary arguments together with more involved machinery from Diophantine approximation. |
| title | More on consecutive multiplicatively dependent triples of integers |
| topic | Number Theory 11N25, 11D61, 11J86 |
| url | https://arxiv.org/abs/2411.12009 |