Modular Schur numbers
For any positive integers l and m, a set of integers is said to be (weakly) l-sum free modulo m if it contains no (pairwise distinct) elements x1, x2, . . . , xl , y satisfying the congruence x1 + . . . + xl ≡ y mod m. It is proved that, for any positive integers k and l, there exists a largest inte...
| Autores: | , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2013 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/136597 |
| Acceso en línea: | https://hdl.handle.net/11441/136597 https://doi.org/10.37236/2374 |
| Access Level: | acceso abierto |
| Palabra clave: | Modular Schur numbers Schur numbers Sum-free sets Weakly sum-free sets |
| Sumario: | For any positive integers l and m, a set of integers is said to be (weakly) l-sum free modulo m if it contains no (pairwise distinct) elements x1, x2, . . . , xl , y satisfying the congruence x1 + . . . + xl ≡ y mod m. It is proved that, for any positive integers k and l, there exists a largest integer n for which the set of the first n positive integers {1, 2, . . . , n} admits a partition into k (weakly) l-sum-free sets modulo m. This number is called the generalized (weak) Schur number modulo m, associated with k and l. In this paper, for all positive integers k and l, the exact value of these modular Schur numbers are determined for m = 1, 2 and 3. |
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