关于帕多万数或佩林数作为以 $$\delta $$ 为基数的三个重数的乘积

Indian Journal of Pure and Applied Mathematics Pub Date : 2024-05-28 DOI:10.1007/s13226-024-00599-z

Pagdame Tiebekabe, Kouèssi Norbert Adédji

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引用次数: 0

摘要

让 $P_m$ 和 $E_m$ 分别是第 m 个帕多万数和佩林数。在本文中，我们证明了对于一个固定的整数 $\delta $ with $\delta \ge 2$ 存在有限多个帕多万数和佩林数，这些数可以表示为基数 $\delta .$ 中三个重数字的乘积，而且，作为一个应用，我们明确地找到了这些数为 $2\le \delta \le 10$ 。

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On Padovan or Perrin numbers as products of three repdigits in base $$\delta $$

Let $P_m$ and $E_m$ be the m-th Padovan and Perrin numbers, respectively. In this paper, we prove that for a fixed integer $\delta $ with $\delta \ge 2$ there exists finitely many Padovan and Perrin numbers that can be represented as products of three repdigits in base $\delta .$ Moreover, we explicitly find these numbers for $2\le \delta \le 10$ as an application.

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Indian Journal of Pure and Applied Mathematics

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