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arXiv · 0801.3639

The sum of irreducible fractions with consecutive denominators is never an integer in a very weak arithmetic

Victor Pambuccian
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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 $PA^-$, in which there is no induction axiom whatsoever.

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Victor Pambuccian. 2008-01-23. The sum of irreducible fractions with consecutive denominators is never an integer in a very weak arithmetic. https://arxiv.org/abs/0801.3639

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