在线性反复序列的质数次数上
Japhet Odjoumani1, Volker Ziegler2
1Institut de Mathématiques et de Sciences Physiques, Université d'Abomey-Calavi, Dangbo, Benin.
Annales mathematiques du Quebec
|October 2, 2023
概括
本研究分析了Diophantine方程U_n = p^x对线性复发序列的分析. 对于大多数质数p,最多有一个解 (n,x),除了特定序列计算的例外.
科学领域:
- 数学理论 数学理论
- 狄奥芬丁方程 狄奥芬丁方程
- 复杂性关系的复杂性关系
背景情况:
- 涉及线性递归序列的二奥芬丁方程是数论的一个丰富领域.
- 了解U_n = p^x的解决方案,可以了解这些序列内的质量次数的分布.
研究的目的:
- 为了研究Diophantine方程U_n = p^x的解决方案数,其中U_n是线性递归序列,p是素数.
- 确定一个给定的素数p的最多存在一个解的条件.
- 计算特殊素数的集合,其中对于特定序列可能存在不止一个解.
主要方法:
- 这项研究采用了来自迪奥芬坦方程理论和线性递归序列的技术.
- 它基于序列U_n的属性建立了边界和条件.
- 计算方法用于识别Tribonacci和Lucas序列的特定异常集.
主要成果:
- 对于满足某些假设的线性递归序列,方程U_n = p^x对于几乎所有质数p的最多有一个解 (n,x).
- 确定了一组有效可计算的例外素数的有限集合.
- 对于Tribonacci序列和Lucas序列加一个的异常集合是明确计算的.
结论:
- 这项研究显著缩小了这种类型的二奥芬丁方程的可能解决方案.
- 这些发现有助于理解线性反复序列内的质量次数.
- 对特定序列的异常集合的明确计算为进一步的理论和计算数理论研究提供了有价值的数据.
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