# Giuga Numbers and the arithmetic derivative

- Published in 2011
- Added on

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We characterize Giuga Numbers as solutions to the equation $n'=an+1$, with $a \in \mathbb{N}$ and $n'$ being the arithmetic derivative. Although this fact does not refute Lava's conjecture, it brings doubts about its veracity.

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## Other information

- key
- Grau2011
- type
- article
- date_added
- 2013-11-15
- date_published
- 2011-03-01

### BibTeX entry

@article{Grau2011, key = {Grau2011}, type = {article}, title = {Giuga Numbers and the arithmetic derivative}, author = {Grau, Jos{\'{e}} Mar{\'{i}}a and Oller-Marc{\'{e}}n, Antonio M.}, abstract = {We characterize Giuga Numbers as solutions to the equation {\$}n'=an+1{\$}, with {\$}a \in \mathbb{\{}N{\}}{\$} and {\$}n'{\$} being the arithmetic derivative. Although this fact does not refute Lava's conjecture, it brings doubts about its veracity.}, comment = {}, date_added = {2013-11-15}, date_published = {2011-03-01}, urls = {http://arxiv.org/abs/1103.2298,http://arxiv.org/pdf/1103.2298v1}, collections = {Unusual arithmetic,Integerology}, month = {mar}, url = {http://arxiv.org/abs/1103.2298 http://arxiv.org/pdf/1103.2298v1}, year = 2011, archivePrefix = {arXiv}, eprint = {1103.2298}, primaryClass = {math.NT}, urldate = {2013-11-15} }