About the Non-Integer Property of Hyperharmonic Numbers

Details About the Non-Integer Property of Hyperharmonic Numbers About the Non-Integer Property of Hyperharmonic Numbers

2008-10-31

arxiv.org/abs/0811.0043v1

Mathematics

Number Theory

7 pages Accepted in Annales Univ. Sci. Budapest., Sect. Math

Scientific paper

It was proven in 1915 by Leopold Theisinger that the $H_n$ harmonic numbers
are never integers. In 1996 Conway and Guy have defined the concept of
hyperharmonic numbers. The question naturally arises: are there any integer
hyperharmonic numbers? The author gives a partial answer to this question and
conjectures that the answer is "no".

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