p、q就是p * a+q * b = c的所有整数解。 相关证明可参考:http://www.cnblogs.com/void/archive/2011/04/18/2020357.html 用扩展欧几里得算法解不定方程ax+by=c; 代码如下: 1bool linear_equation(int a,int b,int c,int &x,int &y)2{3int d=exgcd(a,b,x,y);4if(c%d)5returnfalse;6int...
假设扩展欧几里得算法得到的不定方程k \cdot m+y \cdot m_i=gcd(m,m_i)的解为p,q,那么可以得到k的通解为 k=p \times \frac{a_i-x_0}{gcd(m,m_i)}+\frac{m_i}{gcd(m,m_i)} \times \lambda,\lambda \in \mathbb{Z} \\ 带入x=x_0+k \cdot m就有 \begin{align} x&=x_0+\le...
在中文区讲解这两个算法的博客虽然不少,但是让人看得像是在云里雾里的。 本文通过一个详细的计算过程来讲解辗转相除法(即欧几里得算法),以及拓展的欧几里得算法/Extended Euclidean algorithm。这两个算法有很强的关联,因此请读者先看完辗转相除法再看拓展的欧几里得算法。 辗转相除法(即欧几里得算法) 目的:计算两个...
We know that by means of extended euclidean algorithmxandycan be calculated fromax + by = gcd(a, b).The formula is: x=prev_y;y=prev_x-(a/b)*x; and the code is: intgcd(inta,intb,int&x,int&y){if(b==0){x=1;y=0;returna;}intx1,y1;intd=gcd(b,a%b,x1,y1);x=y1;y=...
欧几里德与扩展欧几里德算法 Extended Euclidean algorithm,欧几里德算法欧几里德算法又称辗转相除法,用于计算两个整数a,b的最大公约数。基本算法:设a=qb+r,其中a,b,q,r都是整数,则gcd(a,b)=gcd(b,r),即gcd(a,b)=gcd(b,a%b)。第一种证明:a可以表示成a=kb+r,则r=a
In this study, basic cryptography terms are mentioned. The RSA algorithm (Rivest-Shamir-Adleman) is the basis of a cryptographic system, a suite of cryptographic algorithms used for private security services or purposes, and this allows public key encryption, widely used to secure pa...
√ ∛ e i π s c t l L ≥ ≤Example of Extended Euclidean AlgorithmRecall that gcd(84, 33) = gcd(33, 18) = gcd(18, 15) = gcd(15, 3) = gcd(3, 0) = 3 We work backwards to write 3 as a linear combination of 84 and 33: 3 = 18 − 15 [Now 3 is a linear ...
euclid-algo refactor adapter to euclids algorithm Jul 1, 2022 .gitignore initial commit extended euclids algorithm Jul 1, 2022 About Implementation of the extended "Euclidean" algorithm. Topics university university-course extended-euclidean-algorithm university-assignment euclidean-algorithm euclid-algorit...
Code README MIT license egcd Pure-Pythonextended Euclidean algorithmimplementation that accepts any number of integer arguments. Installation and Usage This library is available as apackage on PyPI: python -m pip install egcd The library can be imported in the usual way: ...
第四节Extended Euclidean Algorithm and Fundamental Theorem of Arithmetic 扩展欧几里得算法与算术基本定理 第五节Linear Diophantine Equations 线性丢番图方程 第六节Linear Congruences 线性同余(包含中国剩余定理) 第七节The Arithmetic of Z_p Z_p上的计算(包含费马小定理与伪素数) ...