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| Natura: | Preprint |
| Pubblicazione: |
2022
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| Accesso online: | https://arxiv.org/abs/2206.10319 |
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| _version_ | 1866917754461749248 |
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| author | Lopez, Miguel Angel |
| author_facet | Lopez, Miguel Angel |
| contents | In this paper we classify certain values of p that satisfy the Erdos-Straus conjecture, concerning the decomposition of fractions of the form 4/n as sum of three fractions with numerator identically equal to 1, not according to their modular similarity but to the fact that they share solutions with identical structure. We classify all solutions that satisfy that they are of the form (du,dv,duv) and find characterizations for values of p that were initially difficult to classify, such as p=1009. We also study the solutions (x,y,z) that satisfy that gcd(x,y,z)=x and, finally, we classify all the cases in which any of these two variables coincide with each other. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2206_10319 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Structure and form of the solutions of the Erdos-Straus conjecture Lopez, Miguel Angel Number Theory 11D72, 11A07, 11A41 In this paper we classify certain values of p that satisfy the Erdos-Straus conjecture, concerning the decomposition of fractions of the form 4/n as sum of three fractions with numerator identically equal to 1, not according to their modular similarity but to the fact that they share solutions with identical structure. We classify all solutions that satisfy that they are of the form (du,dv,duv) and find characterizations for values of p that were initially difficult to classify, such as p=1009. We also study the solutions (x,y,z) that satisfy that gcd(x,y,z)=x and, finally, we classify all the cases in which any of these two variables coincide with each other. |
| title | Structure and form of the solutions of the Erdos-Straus conjecture |
| topic | Number Theory 11D72, 11A07, 11A41 |
| url | https://arxiv.org/abs/2206.10319 |