关于一个涉及斐波那契数幂的丢番图方程

IF 0.4 4区数学 Q4 MATHEMATICS

Proceedings of the Japan Academy Series A-Mathematical Sciences Pub Date : 2020-04-01 DOI:10.3792/pjaa.96.007

K. Gueth, F. Luca, L. Szalay

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引用次数: 3

摘要

本文研究了关于斐波那契数列加权幂项的丢番图方程F 1 + 2F p 2 + kF p k 1 / 4 F n。对于指数p;q2f1;这个问题已经用特殊的方法解决了，利用等式左边的求和恒等式的性质。在这里，我们提出了一种对任意正整数p和q的统一处理方法，它在实践中适用于小数值。我们得到了p的所有解;q10通过测试新方法。

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 a Diophantine equation involving powers of Fibonacci numbers

This paper deals with the diophantine equation F 1 þ 2F p 2 þ þ kF p k 1⁄4 F n, an equation on the weighted power terms of Fibonacci sequence. For the exponents p; q 2 f1; 2g the problem has already been solved in ad hoc ways using the properties of the summatory identities appear on the left-hand side of the equation. Here we suggest a uniform treatment for arbitrary positive integers p and q which works, in practice, for small values. We obtained all the solutions for p; q 10 by testing the new approach.

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来源期刊

Proceedings of the Japan Academy Series A-Mathematical Sciences 数学-数学

CiteScore

1.00

自引率

0.00%

发文量

审稿时长

6 months

期刊介绍： The aim of the Proceedings of the Japan Academy, Series A, is the rapid publication of original papers in mathematical sciences. The paper should be written in English or French (preferably in English), and at most 6 pages long when published. A paper that is a résumé or an announcement (i.e. one whose details are to be published elsewhere) can also be submitted. The paper is published promptly if once communicated by a Member of the Academy at its General Meeting, which is held monthly except in July and in August.