π曲线和Lebesgue-Nagell方程

IF 0.3 4区数学 Q4 MATHEMATICS

Journal De Theorie Des Nombres De Bordeaux Pub Date : 2023-10-10 DOI:10.5802/jtnb.1254

Michael A. Bennett, Philippe Michaud-Jacobs, Samir Siksek

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引用次数: 0

摘要

对于整数x,q,k,y, n，且k≥0,n≥3。我们通过找到q=41和q=97情况下的所有解扩展了第一和第三作者的工作。我们通过构造一个定义在实二次域K= π (q)上的Frey-Hellegouarch π -曲线，并使用多重frey技术的模方法来实现这一点。

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ℚ-curves and the Lebesgue–Nagell equation

for integers x,q,k,y and n, with k≥0 and n≥3. We extend work of the first and third-named authors by finding all solutions in the cases q=41 and q=97. We do this by constructing a Frey–Hellegouarch ℚ-curve defined over the real quadratic field K=ℚ(q), and using the modular method with multi-Frey techniques.

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来源期刊

Journal De Theorie Des Nombres De Bordeaux MATHEMATICS-

CiteScore

0.60

自引率

0.00%

发文量

期刊介绍： The Journal de Théorie des Nombres de Bordeaux publishes original papers on number theory and related topics (not published elsewhere).