Control is hopeless分享 I just wonder how things are put together and then what happens


孔夫子时代(500 BC)中国古人的数学

已有 1082 次阅读 2021-4-5 11:17 |个人分类:逗我们玩|系统分类:观点评述


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公元前500年中国古人似乎已经知道 $2^p-2$ 可以被素数 $p$ 整除,例如30可以被5整除。这个事实被费马在1640年重新发现,并推广到一般情况,所谓费马小定理。




PS 书中的注释 Chinese 1: G. Реаnо, Formulaire math., 3, Turin, 1901, p. 96, Jeans. 

补充 查了维基的词条 

Chinese hypothesis

In number theory, the Chinese hypothesis is a disproven conjecture stating that an integer $n$ is prime if and only if it satisfies the condition that $2^n-2$ is divisible by $n$—in other words, that integer $n$ is prime if and only if $2^n\equiv 2 ~\text{mod}~  n$. It is true that if $n$ is prime, then $2^n\equiv 2 ~\text{mod}~  n$ (this is a special case of Fermat's little theorem). However, the converse (if $2^n\equiv 2 ~\text{mod}~  n$ then $n$ is prime) is false, and therefore the hypothesis as a whole is false. The smallest counter example is $n=341=11\times 31$. Composite numbers $n$ for which $2^n-2$ is divisible by $n$ are called Poulet numbers. They are a special class of Fermat pseudoprimes.


Once, and sometimes still, mistakenly thought to be of ancient Chinese origin, the Chinese hypothesis actually originates in the mid-19th century from the work of Qing dynasty mathematician Li Shanlan (1811–1882).[1] He was later made aware his statement was incorrect and removed it from his subsequent work but it was not enough to prevent the false proposition from appearing elsewhere under his name;[1] a later mistranslation in the 1898 work of Jeans dated the conjecture to Confucian times and gave birth to the ancient origin myth.[1][2]



12 郑永军 尤明庆 宁利中 刘全慧 杨正瓴 王安良 史晓雷 武夷山 李学宽 刘钢 李毅伟 李楠

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