On the multiplicity in Pillai's problem with Fibonacci numbers and powers of a fixed prime

Pub Date : 2022-07-24 DOI:10.3336/gm.57.2.02

Herbert Batte, Mahadi Ddamulira, Juma Kasozi, F. Luca

引用次数: 2

Abstract

Let \( \{F_n\}_{n\geq 0} \) be the sequence of Fibonacci numbers and let \(p\) be a prime. For an integer \(c\) we write \(m_{F,p}(c)\) for the number of distinct representations of \(c\) as \(F_k-p^\ell\) with \(k\ge 2\) and \(\ell\ge 0\). We prove that \(m_{F,p}(c)\le 4\).

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关于皮莱的斐波那契数和定素数幂问题的多重性

设\( \{F_n\}_{n\geq 0} \)为斐波那契数列，设\(p\)为素数。对于整数\(c\)，我们将\(c\)的不同表示形式的数量写成\(m_{F,p}(c)\)，例如\(F_k-p^\ell\)与\(k\ge 2\)和\(\ell\ge 0\)。我们证明\(m_{F,p}(c)\le 4\)。

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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