Some Methods of Erdős Applied to Finite Arithmetic Progressions

T. N. Shorey () and Robert Tijdeman ()
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T. N. Shorey: Tata Institute of Fundamental Research, School of Mathematics
Robert Tijdeman: Leiden University, Mathematical Institute

A chapter in The Mathematics of Paul Erdős I, 2013, pp 269-287 from Springer

Abstract: Summary. Since 1934 Erdős has introduced various methods to derive arithmetic properties of blocks of consecutive integers. This research culminated in 1975 when Erdős and Selfridge (Ill J Math 19:292–301, 1975) established the old conjecture that the product of two or more consecutive positive integers is never a perfect power. It is very likely that the product of the terms of a finite arithmetic progression of length at least four is never a perfect power. In the present paper it is shown how Erdős’ methods have been extended to obtain results for arithmetic progressions.

Keywords: Prime Factor; Arithmetic Progression; Absolute Constant; Black Vertex; White Vertex (search for similar items in EconPapers)
Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4614-7258-2_18

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DOI: 10.1007/978-1-4614-7258-2_18

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