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2008 The Sum of Irreducible Fractions with Consecutive Denominators Is Never an Integer in PA-
Victor Pambuccian
Notre Dame J. Formal Logic 49(4): 425-429 (2008). DOI: 10.1215/00294527-2008-021

Abstract

Two results of elementary number theory, going back to Kürschák and Nagell, stating that the sums i=1 k mi n+i (with k1, ( mi ,n+i)=1, mi <n+i) and i=0 k 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.

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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

Information

Published: 2008
First available in Project Euclid: 17 October 2008

zbMATH: 1185.03086
MathSciNet: MR2456657
Digital Object Identifier: 10.1215/00294527-2008-021

Subjects:
Primary: 03C62
Secondary: 03B30, 11A05

Rights: Copyright © 2008 University of Notre Dame

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