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Some Methods of Erdős Applied to Finite Arithmetic Progressions

In: The Mathematics of Paul Erdős I

Author

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  • T. N. Shorey

    (Tata Institute of Fundamental Research, School of Mathematics)

  • Robert Tijdeman

    (Leiden University, Mathematical Institute)

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.

Suggested Citation

  • T. N. Shorey & Robert Tijdeman, 2013. "Some Methods of Erdős Applied to Finite Arithmetic Progressions," Springer Books, in: Ronald L. Graham & Jaroslav Nešetřil & Steve Butler (ed.), The Mathematics of Paul Erdős I, edition 2, pages 269-287, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4614-7258-2_18
    DOI: 10.1007/978-1-4614-7258-2_18
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