The sum of irreducible fractions with consecutive denominators is never an integer in a very weak arithmetic
Logic
2008-01-24 v1 Number Theory
Abstract
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 , in which there is no induction axiom whatsoever.
Keywords
Cite
@article{arxiv.0801.3639,
title = {The sum of irreducible fractions with consecutive denominators is never an integer in a very weak arithmetic},
author = {Victor Pambuccian},
journal= {arXiv preprint arXiv:0801.3639},
year = {2008}
}