%0 Journal Article
%T The sum of irreducible fractions with consecutive denominators is never an integer in a very weak arithmetic
%A Victor Pambuccian
%J Mathematics
%D 2008
%I arXiv
%X Two theorems of elmentary arithmetic, one stating that the sum of the reciprocals of any number of consecutive positive integers is never an integer, and a generalization thereof by Trygve Nagell, are shown to be provable inside a very weak arithmetic, Richard Kaye's $PA^-$, in which there is no induction axiom whatsoever.
%U http://arxiv.org/abs/0801.3639v1