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Diophantine equations in separated variables and polynomial power sums
We consider Diophantine equations of the shape [Formula: see text] , where the polynomials f and g are elements of power sums. Using a finiteness criterion of Bilu and Tichy, we will prove that under suitable assumptions infinitely many rational solutions (x, y) with a bounded denominator are only p...
| Autores principales: | , |
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| Formato: | Online Artículo Texto |
| Lenguaje: | English |
| Publicado: |
Springer Vienna
2021
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| Materias: | |
| Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8550583/ https://www.ncbi.nlm.nih.gov/pubmed/34776538 http://dx.doi.org/10.1007/s00605-021-01560-6 |
| Sumario: | We consider Diophantine equations of the shape [Formula: see text] , where the polynomials f and g are elements of power sums. Using a finiteness criterion of Bilu and Tichy, we will prove that under suitable assumptions infinitely many rational solutions (x, y) with a bounded denominator are only possible in trivial cases. |
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