Report
On differences of perfect powers and prime powers
| العنوان: | On differences of perfect powers and prime powers |
|---|---|
| المؤلفون: | García, Pedro-José Cazorla |
| سنة النشر: | 2023 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Number Theory, 11D61 (primary) 11D41, 11D59, 11F80, 11F11 (secondary) |
| الوصف: | Given a prime number $q$ and a squarefree integer $C_1$, we develop a method to explicitly determine the tuples $(y, n, \alpha)$ for which the difference $y^n-q^\alpha$ has squarefree part equal to $C_1$. Our techniques include the combination of the local information provided by Galois representations of Frey-Hellegouarch curves with the effective resolution of Thue-Mahler equations, as well as the use of improved lower bounds for $q-$adic and complex logarithms. As an application of this methodology, we will completely resolve the case when $1 \le C_1 \le 20$ and $ 2 \le q < 25$. Comment: 40 pages |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2312.09985 |
| رقم الانضمام: | edsarx.2312.09985 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |