在Pillai的问题上涉及第二种类型的卢卡斯序列
Sebastian Heintze1, Volker Ziegler2
1Institute of Analysis and Number Theory, Graz University of Technology, Steyrergasse 30/II, A-8010 Graz, Austria.
Research in number theory
|May 16, 2024
概括
这项研究分析了涉及卢卡斯-莱默序列的二奥芬丁方程. 如果解决方案很丰富,我们就为解决方案大小和多项式系数设定了界限.
科学领域:
- 数学理论 数学理论
- 代数数字理论的代数理论.
背景情况:
- 狄奥芬丁方程是数论的基础,寻求整数解决方案.
- 第二种卢卡斯-莱默序列是特定的整数序列,在初始性测试和密码学中具有应用.
研究的目的:
- 为了研究狄奥芬丁方程V_n - b^m = c.
- 为了确定这个方程的解决方案的边界性条件.
主要方法:
- 迪奥芬丁方程的分析.
- 第二种卢卡斯-莱默序列的属性.
- 数学理论技术用于建立边界.
主要成果:
- 证明在特定条件下,如果狄奥芬丁方程V_n - b^m = c至少有三个解 (n,m),那么存在一个上限.
- 确定了这些溶液的大小的上限 (n,m).
- 导出了V_n的特征多项式的系数的上限.
结论:
- 对狄奥芬丁方程V_n - b^m = c存在多个解,这意味着对解数的限制.
- 这项研究有助于理解涉及特定重复序列的迪奥芬坦方程的行为.
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