Almost perfect powers in products of consecutive integers

K. Györy, Á Pintér

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

The classical equations (1) and (3) have a very extensive literature. The main purpose of recent investigations is to solve these equations with as large bound for the greatest prime factor P(b) of b as possible. General elementary methods have been developed for studying (1) and (3) which, however, cannot be applied if k is small. As a generalization of previous results obtained for small values of k, we completely solve Eq. (1) for k ≤ 5, under the assumption that P(b) ≤ p k , the k-th prime (cf. Theorem 1). A similar result is established for Eq. (3) (cf. Theorem 2). In our proofs, several deep results and powerful techniques are combined from modern Diophantine analysis.

Original languageEnglish
Pages (from-to)19-33
Number of pages15
JournalMonatshefte fur Mathematik
Volume145
Issue number1
DOIs
Publication statusPublished - May 2005

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Consecutive
Integer
Prime factor
Theorem
Generalization

Keywords

  • Binomial Thue equations
  • Exponential diophantine equations
  • Product of consecutive integers

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Almost perfect powers in products of consecutive integers. / Györy, K.; Pintér, Á.

In: Monatshefte fur Mathematik, Vol. 145, No. 1, 05.2005, p. 19-33.

Research output: Contribution to journalArticle

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