The sum of irreducible fractions with consecutive denominators is never an integer in PA-

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Abstract

Two results of elementary number theory, going back to Kürschák and Nagell, stating that the sums Σik=1 mi/n+i (with k ≥ 1, (mi,n + i) = 1, mi < n + i) and Σik=0 1/m+in (with n, m, k positive integers) are never integers, are shown to hold in PA-, a very weak arithmetic, whose axiom system has no induction axiom.

Original languageEnglish (US)
Pages (from-to)425-429
Number of pages5
JournalNotre Dame Journal of Formal Logic
Volume49
Issue number4
DOIs
StatePublished - Dec 1 2008

Keywords

  • Kaye's PA
  • Kürschák's theorem
  • Nagell's theorem
  • Weak arithmetic

ASJC Scopus subject areas

  • Logic

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