Comptes Rendus
Number Theory
Hyperharmonic integers exist
Comptes Rendus. Mathématique, Volume 358 (2020) no. 11-12, pp. 1179-1185.

We show that there exist infinitely many hyperharmonic integers, and this refutes a conjecture of Mező. In particular, for r=64·(2 α -1)+32, the hyperharmonic number h 33 (r) is integer for 153 different values of α(mod748440), where the smallest r is equal to 64·(2 2659 -1)+32.

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Accepted:
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DOI: 10.5802/crmath.137
Classification: 11B83, 05A10, 11B75

Doğa Can Sertbaş 1

1 Department of Mathematics, Faculty of Sciences, Sivas Cumhuriyet University, 58140, Sivas, TURKEY.
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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Doğa Can Sertbaş. Hyperharmonic integers exist. Comptes Rendus. Mathématique, Volume 358 (2020) no. 11-12, pp. 1179-1185. doi : 10.5802/crmath.137. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.137/

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