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

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

2008-01-23

arxiv.org/abs/0801.3639v1

Mathematics

Logic

Scientific paper

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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