Solutions to $\sum_{i=1}^n 1/x_i=1$ in integers $p^a\,q^b$ with $p$ and $q$ two set primes
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arXiv
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866912868377559040 |
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| author | Levaillant, Claire I. |
| author_facet | Levaillant, Claire I. |
| contents | We present an algorithm for computing all the solutions in not necessarily distinct integers to the decomposition of the unit into a sum of unit fractions with denominators $p^a.q^b$ where $p$ and $q$ are two distinct primes, each appearing at least once in the solution. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_02012 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Solutions to $\sum_{i=1}^n 1/x_i=1$ in integers $p^a\,q^b$ with $p$ and $q$ two set primes Levaillant, Claire I. Number Theory Combinatorics 11D68, 11B75 We present an algorithm for computing all the solutions in not necessarily distinct integers to the decomposition of the unit into a sum of unit fractions with denominators $p^a.q^b$ where $p$ and $q$ are two distinct primes, each appearing at least once in the solution. |
| title | Solutions to $\sum_{i=1}^n 1/x_i=1$ in integers $p^a\,q^b$ with $p$ and $q$ two set primes |
| topic | Number Theory Combinatorics 11D68, 11B75 |
| url | https://arxiv.org/abs/2602.02012 |