Some monochromatic patterns in natural numbers
Fuente:
arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910208324796416 |
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| author | Ghosh, Arpita Ghosh, Surojit |
| author_facet | Ghosh, Arpita Ghosh, Surojit |
| contents | The set of sums of two squares plays a significant role in elementary number theory. In this article, we establish the existence of several rich monochromatic configurations in the natural numbers by exploiting algebraic structures induced by the set of sums of two squares. The proofs rely largely on the algebraic properties arising from the induced structures on the Stone-Čech compactification of the natural numbers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_14066 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Some monochromatic patterns in natural numbers Ghosh, Arpita Ghosh, Surojit Combinatorics 05D10, 05C55, 22A15 The set of sums of two squares plays a significant role in elementary number theory. In this article, we establish the existence of several rich monochromatic configurations in the natural numbers by exploiting algebraic structures induced by the set of sums of two squares. The proofs rely largely on the algebraic properties arising from the induced structures on the Stone-Čech compactification of the natural numbers. |
| title | Some monochromatic patterns in natural numbers |
| topic | Combinatorics 05D10, 05C55, 22A15 |
| url | https://arxiv.org/abs/2411.14066 |