Wilson's Theorem

【Wilson's Theorem】的更多相关文章

ProofsSuppose first that $p$ is composite. Then $p$ has a factor $d > 1$ that is less than or equal to $p-1$. Then $d$ divides $(p-1)!$, so $d$ does not divide $(p-1)! + 1$. Therefore $p$ does not divide $(p-1)! + 1$. Two proofs of the converse are p…

Wilson's theorem在RSA题中运用

引言最近一段时间在再练习数论相关的密码学题目,自己之前对于数论掌握不是很熟练,借此机会先对数论基本的四大定理进行练习这次的练习时基于Wilson's theorem(威尔逊定理)在RSA题目中的练习最近几次比赛中这个定理出现频率挺高的,正好之前Rocarctf中有一道题考到了这个定理这次就用于练习 Wilson's theorem简介 P 为质数 <==>(P−1)!≡ −1(mod P) 推论 & 变形式: (p-1)! + (p-2) != p * (p-2)! (p-1)!…

The Hundred Greatest Theorems

The Hundred Greatest Theorems The millenium seemed to spur a lot of people to compile "Top 100" or "Best 100" lists of many things, including movies (by the American Film Institute) and books (by the Modern Library). Mathematicians wer…

Parseval's theorem 帕塞瓦尔定理

Source: wiki: Parseval's theorem As for signal processing, the power within certain frequency band = the sum of (power spectrum at all frequencies within the frequency band)^2.…

利用Cayley-Hamilton theorem 优化矩阵线性递推

平时有关线性递推的题,很多都可以利用矩阵乘法来解决. 时间复杂度一般是O(K3logn)因此对矩阵的规模限制比较大. 下面介绍一种利用利用Cayley-Hamilton theorem加速矩阵乘法的方法. Cayley-Hamilton theorem: 记矩阵A的特征多项式为f(x). 则有f(A)=0. 证明可以看维基百科 https://en.wikipedia.org/wiki/Cayley–Hamilton_theorem#A_direct_algebraic_proof 另外我在高…

Kernel Methods (6) The Representer Theorem

The Representer Theorem, 表示定理. 给定: 非空样本空间: $\chi$ $m$个样本:$\{(x_1, y_1), \dots, (x_m, y_m)\}, x_i in \chi, y_i \in R$ 非负的损失函数: $J:(\chi \times R^2)^m \to R^+$. 这个符号表示初看挺别扭的, 从wikipedia上抄来的. 含义是$J$有$m \times 3$个参数, 3代表: 样本$x_i$ (一个\(\chi\…

加州大学伯克利分校Stat2.2x Probability 概率初步学习笔记: Section 4 The Central Limit Theorem

Stat2.2x Probability(概率)课程由加州大学伯克利分校(University of California, Berkeley)于2014年在edX平台讲授. PDF笔记下载(Academia.edu) Summary Standard Error The standard error of a random variable $X$ is defined by $$SE(X)=\sqrt{E((X-E(X))^2)}$$ $SE$ measures the rough size…