Perfect powers in products with consecutive terms from arithmetic progressions, II

Research output: Chapter in Book/Report/Conference proceedingChapter

1 Citation (Scopus)

Abstract

There is a very rich literature on perfect powers or almost perfect powers in products of the form m(m + d) …: (m + (k − 1)d), where m, d are coprime positive integers and k ≥ 3. By a conjecture, such a product is never a perfect n-th power if k > 3, n ≥2 or k = 3, n > 2. In the classical case d = 1 the conjecture has been proved by Erdős and Selfridge [11]. The general case d ≥ 1 seems to be very hard, then there are only partial results; for survey papers on results obtained before 2006 we refer to Tijdeman [46]– [48], Shorey and Tijdeman [43, 44], Shorey [38]–[42]_and Győry [15, 16].

Original languageEnglish
Title of host publicationBolyai Society Mathematical Studies
PublisherSpringer Berlin Heidelberg
Pages311-324
Number of pages14
DOIs
Publication statusPublished - Jan 1 2013

Publication series

NameBolyai Society Mathematical Studies
Volume25
ISSN (Print)1217-4696

    Fingerprint

ASJC Scopus subject areas

  • Computational Theory and Mathematics
  • Applied Mathematics

Cite this

Győry, K. (2013). Perfect powers in products with consecutive terms from arithmetic progressions, II. In Bolyai Society Mathematical Studies (pp. 311-324). (Bolyai Society Mathematical Studies; Vol. 25). Springer Berlin Heidelberg. https://doi.org/10.1007/978-3-642-39286-3_10