English

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 PAPA^-, 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}
}