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Wed Feb 15 10:27:02 HKT 2017
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scateu committed Feb 15, 2017
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Expand Up @@ -151,13 +151,16 @@ $$ (m^e)^d \equiv m \mod pq $$
#### 3. 依赖的定理


费马小定理: ($p$为素数, 且$p$不整除$a$. )
**费马小定理:**

([这里](https://mp.weixin.qq.com/s?__biz=MzA3OTgzMzUzOA==&mid=2651227431&idx=1&sn=8a249975b3b754b062a9f998eb111338&chksm=845f558ab328dc9c200db932866abd363a5b284e35f72c7317aa2329c9d7b003339724cbe735&mpshare=1&scene=1&srcid=02155ICQJ3eATKwRpgHvufkN&pass_ticket=9%2F4JlZH6VGedHYRK2ggZ1a04q%2FglG9kWCUNTWLKKdauf91Rr3tjyz8UPyKamAyJS#rd)有一个很有趣的证明,物理学家给出的,使用伊辛自旋(Ising spin)证明,但实际上不理解这个概念也无所谓,用小学几何知识就够了)
([这里](https://mp.weixin.qq.com/s?__biz=MzA3OTgzMzUzOA==&mid=2651227431&idx=1&sn=8a249975b3b754b062a9f998eb111338&chksm=845f558ab328dc9c200db932866abd363a5b284e35f72c7317aa2329c9d7b003339724cbe735&mpshare=1&scene=1&srcid=02155ICQJ3eATKwRpgHvufkN&pass_ticket=9%2F4JlZH6VGedHYRK2ggZ1a04q%2FglG9kWCUNTWLKKdauf91Rr3tjyz8UPyKamAyJS#rd)有一个很有趣的证明,物理学家给出的,使用伊辛自旋(Ising spin)证明,但实际上不理解这个概念也无所谓,用小学几何知识就够了。证明出自: H. Gutfreund and W. A. Little, Am. J. Phys.50(3), 1982.)

($p$为素数, 且$p$不整除$a$. )

$$ a^{p-1} \equiv 1 \mod p $$

中国剩余定理(CRT: Chinese Remainder Theorem):
**中国剩余定理(CRT: Chinese Remainder Theorem):**

简言之, 给出了同余方程组的解:

> 今有物不知其数, 三三数之剩二, 五五数之剩三, 七七数之剩二, 问物几何?
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