A Note on The Gaussian Moat Problem
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2019
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| _version_ | 1866909306966769664 |
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| author | Das, Madhuparna |
| author_facet | Das, Madhuparna |
| contents | The Gaussian moat problem asks whether it is possible to find an infinite sequence of distinct Gaussian prime numbers such that the difference between consecutive numbers in the sequence is bounded. In this paper, we have proved that the answer is `No', that is an infinite sequence of distinct Gaussian prime numbers can not be bounded by an absolute constant, for the Gaussian primes $p=a^2+b^2$ with $a,b\neq0$. We consider each prime $(a,b)$ as a lattice point on the complex plane and use their properties to prove the main result. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1908_10392 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | A Note on The Gaussian Moat Problem Das, Madhuparna Number Theory 11A41, 11N05, 68R05 The Gaussian moat problem asks whether it is possible to find an infinite sequence of distinct Gaussian prime numbers such that the difference between consecutive numbers in the sequence is bounded. In this paper, we have proved that the answer is `No', that is an infinite sequence of distinct Gaussian prime numbers can not be bounded by an absolute constant, for the Gaussian primes $p=a^2+b^2$ with $a,b\neq0$. We consider each prime $(a,b)$ as a lattice point on the complex plane and use their properties to prove the main result. |
| title | A Note on The Gaussian Moat Problem |
| topic | Number Theory 11A41, 11N05, 68R05 |
| url | https://arxiv.org/abs/1908.10392 |