关于广义Lucas序列的一些新结果

IF 0.8 4区数学 Q2 MATHEMATICS

Analele Stiintifice Ale Universitatii Ovidius Constanta-Seria Matematica Pub Date : 2021-03-01 DOI:10.2478/auom-2021-0002

D. Andrica, O. Bagdasar, George C. Ţurcaş

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引用次数: 0

摘要

本文引入了计算不超过给定值x的广义Lucas和Pell-Lucas序列项个数的函数，并在一定条件下导出了它们的精确公式(定理3和定理4)，建立了它们的渐近极限(定理6)，给出了a- fibonacci和a-Lucas序列项的充分必要算术条件。最后，利用西格尔的一个深度定理，证明了上述数列只包含有限多个完美幂。在此过程中，我们还发现了一些新的整数序列。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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On some new results for the generalised Lucas sequences

Abstract In this paper we introduce the functions which count the number of generalized Lucas and Pell-Lucas sequence terms not exceeding a given value x and, under certain conditions, we derive exact formulae (Theorems 3 and 4) and establish asymptotic limits for them (Theorem 6). We formulate necessary and sufficient arithmetic conditions which can identify the terms of a-Fibonacci and a-Lucas sequences. Finally, using a deep theorem of Siegel, we show that the aforementioned sequences contain only finitely many perfect powers. During the process we also discover some novel integer sequences.

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来源期刊

Analele Stiintifice Ale Universitatii Ovidius Constanta-Seria Matematica MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： This journal is founded by Mirela Stefanescu and Silviu Sburlan in 1993 and is devoted to pure and applied mathematics. Published by Faculty of Mathematics and Computer Science, Ovidius University, Constanta, Romania.