On a variant of Pillai’s problem with factorials and S-units

IF 0.6 3区数学 Q3 MATHEMATICS Ramanujan Journal Pub Date : 2023-10-24 DOI:10.1007/s11139-023-00787-1

Bernadette Faye, Florian Luca, Volker Ziegler

引用次数: 0

Abstract

Abstract Let S be a finite, fixed set of primes. In this paper, we show that the set of integers c which have at least two representations as a difference between a factorial and an S -unit is finite and effectively computable. In particular, we find all integers that can be written in at least two ways as a difference of a factorial and an S -unit associated with the set of primes $$\{2,3,5,7\}$$ { 2 , 3 , 5 , 7 } .

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关于阶乘和s单位的皮莱问题的一个变体

设S是一个有限的、固定的素数集合。在本文中，我们证明了在阶乘和S -单位之间至少有两种表示的整数集c是有限且有效可计算的。特别地，我们找到了所有的整数，这些整数可以用至少两种方式写成阶乘和S -单位的差与质数集$$\{2,3,5,7\}$$ 2, 3, 5, 7{相关。}

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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来源期刊

Ramanujan Journal 数学-数学

CiteScore

1.40

自引率

14.30%

发文量

133

审稿时长

6-12 weeks

期刊介绍： The Ramanujan Journal publishes original papers of the highest quality in all areas of mathematics influenced by Srinivasa Ramanujan. His remarkable discoveries have made a great impact on several branches of mathematics, revealing deep and fundamental connections. The following prioritized listing of topics of interest to the journal is not intended to be exclusive but to demonstrate the editorial policy of attracting papers which represent a broad range of interest: Hyper-geometric and basic hyper-geometric series (q-series) * Partitions, compositions and combinatory analysis * Circle method and asymptotic formulae * Mock theta functions * Elliptic and theta functions * Modular forms and automorphic functions * Special functions and definite integrals * Continued fractions * Diophantine analysis including irrationality and transcendence * Number theory * Fourier analysis with applications to number theory * Connections between Lie algebras and q-series.