Egyptian fractions for few primes
Fuente:
arXiv
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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866908434569363456 |
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| author | Czenky, Agustina McGovern, Emily Plavnik, Julia Rowell, Eric Watkins, Abigail |
| author_facet | Czenky, Agustina McGovern, Emily Plavnik, Julia Rowell, Eric Watkins, Abigail |
| contents | We study solutions to the Egyptian fractions equation with the prime factors of the denominators constrained to lie in a fixed set of primes. We evaluate the effectiveness of the greedy algorithm in establishing bounds on such solutions. Additionally, we present improved algorithms for generating low-rank solutions and solutions restricted to specific prime sets. Computational results obtained using these algorithms are provided, alongside a discussion on their performance. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_03727 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Egyptian fractions for few primes Czenky, Agustina McGovern, Emily Plavnik, Julia Rowell, Eric Watkins, Abigail Number Theory 11D68, 18M20 We study solutions to the Egyptian fractions equation with the prime factors of the denominators constrained to lie in a fixed set of primes. We evaluate the effectiveness of the greedy algorithm in establishing bounds on such solutions. Additionally, we present improved algorithms for generating low-rank solutions and solutions restricted to specific prime sets. Computational results obtained using these algorithms are provided, alongside a discussion on their performance. |
| title | Egyptian fractions for few primes |
| topic | Number Theory 11D68, 18M20 |
| url | https://arxiv.org/abs/2507.03727 |