Browsing by Author "Goral, Haydar"
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Almost all hyperharmonic numbers are not integers
Goral, Haydar; Sertbas, Doga Can (ACADEMIC PRESS INC ELSEVIER SCIENCE, 2017)It is an open question asked by Mezo that there is no hyperharmonic integer except 1. So far it has been proved that all hyperharmonic numbers are not integers up to order r = 25. In this paper, we extend the current results ... -
A congruence for some generalized harmonic type sums
Goral, Haydar; Sertbas, Doga Can (WORLD SCIENTIFIC PUBL CO PTE LTD, 2018)In 1862, Wolstenholme proved that the numerator of the (p - 1)th harmonic number is divisible by p(2) for any prime p >= 5. A variation of this theorem was shown by Alkan and Leudesdorf. Motivated by these results, we prove ... -
DENSITY AND FINITENESS RESULTS ON SUMS OF FRACTIONS
Goral, Haydar; Sertbas, Doga Can (AMER MATHEMATICAL SOC, 2019)We show that the height density of a finite sum of fractions is zero. In fact, we give quantitative estimates in terms of the height function. Then, we focus on the unit fraction solutions in the ring of integers of a given ...