Two games on arithmetic functions: SALIQUANT and NONTOTIENT
Issued Date
2023-01-01
Resource Type
eISSN
26642557
Scopus ID
2-s2.0-85188207004
Journal Title
Discrete Mathematics Letters
Volume
12
Start Page
209
End Page
216
Rights Holder(s)
SCOPUS
Bibliographic Citation
Discrete Mathematics Letters Vol.12 (2023) , 209-216
Suggested Citation
Ellis P., Shi J., Thanatipanonda T.A., Tu A. Two games on arithmetic functions: SALIQUANT and NONTOTIENT. Discrete Mathematics Letters Vol.12 (2023) , 209-216. 216. doi:10.47443/dml.2023.154 Retrieved from: https://repository.li.mahidol.ac.th/handle/20.500.14594/97751
Title
Two games on arithmetic functions: SALIQUANT and NONTOTIENT
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Abstract
We investigate the Sprague-Grundy sequences for two normal-play impartial games based on arithmetic functions, first described by Iannucci and Larsson in a book chapter. In each game, the set of positions is N. In saliquant, the options are to subtract a non-divisor. Here we obtain several nice number theoretic lemmas, a fundamental theorem, and two conjectures about the eventual density of Sprague-Grundy values. In nontotient, the only option is to subtract the number of relatively prime residues. Here we are able to calculate certain Sprague-Grundy values and start to understand an appropriate class function.