喵喵把扩展欧几里得算法解同余方程组的代码贴在下面啦,还没有理解上面的推导过程的猫猫可以尝试着通过代码来理解哦! #include<stdio.h>#include<ctype.h>#include<iostream>#define maxN 10usingnamespacestd;inlinelonglongread(longlongx=0,boolflag=0,charc=0)
设c是a,b的最大公约数,即c=gcd(a,b),则有 a=mc,b=nc,其中m,n为正整数,且m,n互为质数 由r= a mod b可知,r= a- qb 其中,q是正整数, 则r=a-qb=mc-qnc=(m-qn)c b=nc,r=(m-qn)c,且n,(m-qn)互质(假设n,m-qn不互质,则n=xd, m-qn=yd 其中x,y,d都是正整数,且d>1 则a=...
Extended euclidean algorithmLarge-scale polynomialsCloud computing gives resource-constrained clients great conveniences to outsource exorbitant computations to a public cloud. The extended Euclidean algorithm with large-scale polynomials over finite fields is fundamental and widespread in computer science and ...
Extended Euclidean Algorithm (https://www.mathworks.com/matlabcentral/fileexchange/32852-extended-euclidean-algorithm), MATLAB Central File Exchange. Retrieved June 6, 2025. MATLAB Release Compatibility Created with R2008a Compatible with any release Platform Compatibility Windows macOS Linux Others ...
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...
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。
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
This is how I do it, it's not most efficient way but it's in my opinion a very clear and easy way to remember. ax + by = c works when c is a multiple of gcd(a,b) Be careful of cases where a = 0 or b = 0 or both ...
√ ∛ 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 ...
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) ...