On two four term arithmetic progressions with equal product

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Abstract

We investigate when two four-term arithmetic progressions have an equal product of their terms. This is equivalent to studying the (arithmetic) geometry of a non-singular quartic surface. It turns out that there are many polynomial parametrizations of such progressions, and it is likely that there exist polynomial parametrizations of every positive degree. We find all such parametrizations for degrees 1 to 4, and give examples of parametrizations for degrees 5 to 10.

Original languageEnglish (US)
Pages (from-to)39-55
Number of pages17
JournalAnnales Mathematicae et Informaticae
Volume52
DOIs
StatePublished - 2020

ASJC Scopus subject areas

  • Computer Science(all)
  • Mathematics(all)

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