Abstract
Two results of elementary number theory, going back to Kürschák and Nagell, stating that the sums ∑ki=1min+i (with k≥1, (mi,n+i)=1, mi<n+i) and ∑ki=01m+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.
Citation
Victor Pambuccian. "The Sum of Irreducible Fractions with Consecutive Denominators Is Never an Integer in PA-." Notre Dame J. Formal Logic 49 (4) 425 - 429, 2008. https://doi.org/10.1215/00294527-2008-021
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