A class of exponential congruences in several variables

Geumlan Choi, Alexandru Zaharescu

Research output: Contribution to journalArticlepeer-review

Abstract

A problem raised by Selfridge and solved by Pomerance asks to find the pairs (a, b) of natural numbers for which 2a - 2b divides na - nb for all integers n. Vajaitu and one of the authors have obtained a generalization which concerns elements α1,..., αk and β in the ring of integers A of a number field for which ∑i=1k αiβai divides ∑i=1k αizai for any z ∈ A. Here we obtain a further generalization, proving the corresponding finiteness results in a multidimensional setting.

Original languageEnglish (US)
Pages (from-to)717-735
Number of pages19
JournalJournal of the Korean Mathematical Society
Volume41
Issue number4
DOIs
StatePublished - 2004

Keywords

  • Algebraic integers
  • Exponential congruences
  • Polynomials of several variables

ASJC Scopus subject areas

  • Mathematics(all)

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