k-Pell 和 Tribonacci 数的常用术语

IF 1 Q1 MATHEMATICS

European Journal of Pure and Applied Mathematics Pub Date : 2024-01-31 DOI:10.29020/nybg.ejpam.v17i1.4989

Hunar Taher, Saroj Kumar Dash

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引用次数: 0

摘要

设 Tm 为 Tribonacci 数列，k-Pell 数列是 k ≥ 2 时 Pell 数列的一般化。前 k 项分别为 0，0，...，0，1，而前项之后的每项都由线性递归 P (k) n = 2P (k) n-1 + P (k) n-2 + ... 定义。+ P (k) n-k 。我们研究 k ≥ 2 的正整数 (n, k, m) 的二叉方程 P (k) n = Tm 的解。我们利用代数数对数线性形式的下界与续分数理论。

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Common Terms of k-Pell and Tribonacci Numbers

Let Tm be a Tribonacci sequence, and let the k-Pell sequence be a generalization of the Pell sequence for k ≥ 2 . The first k terms are 0, 0, ..., 0, 1, and each term after the forewords is defined by linear recurrence P (k) n = 2P (k) n−1 + P (k) n−2 + ... + P (k) n−k . We study the solution of the Diophantine equation P (k) n = Tm for the positive integer (n, k, m) with k ≥ 2. We use the lower bound for linear forms in logarithms of algebraic numbers with the theory of the continued fraction.

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来源期刊

European Journal of Pure and Applied Mathematics MATHEMATICS-

CiteScore

1.30

自引率

28.60%

发文量

156