Taiwanese Journal of Mathematics

ON THE MYTH OF AN ANCIENT CHINESE THEOREM ABOUT PRIMALITY

Qi Han and Man-Keung Siu

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Abstract

In the western world there is this myth that the ancient Chinese knew a special case of Fermat's Little Theorem and erroneously took it as a criterion for primality, namely, that $n$ is a prime if and only if $2^{n-]} -1$ is divisible by $n$. This article discusses how this myth might have come about, in particular tells the story of an investigation on number theory by Li Shanlan in the mid $19^{\rm th}$ century. The discussion touches upon the social history of the incident in connection with the polarized attitude different foreigners took towards Chinese mathematics at the time.

Article information

Source
Taiwanese J. Math., Volume 12, Number 4 (2008), 941-949.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500404988

Digital Object Identifier
doi:10.11650/twjm/1500404988

Mathematical Reviews number (MathSciNet)
MR2426538

Zentralblatt MATH identifier
1181.01008

Subjects
Primary: 01A25: China 01A55: 19th century 11A07: Congruences; primitive roots; residue systems 11A51: Factorization; primality

Keywords
Carmichael number Fermat's Little Theorem Li Shanlan

Citation

Han, Qi; Siu, Man-Keung. ON THE MYTH OF AN ANCIENT CHINESE THEOREM ABOUT PRIMALITY. Taiwanese J. Math. 12 (2008), no. 4, 941--949. doi:10.11650/twjm/1500404988. https://projecteuclid.org/euclid.twjm/1500404988


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