扩展欧几里得算法(Extended Euclidean algorithm)是欧几里得算法(又叫辗转相除法)的扩展。已知整数a、b,扩展欧几里得算法可以在求得a、b的最大公约数的同时,能找到整数x、y,使它们满足贝祖等式 演算过程 求二元一次不定方程 的整数解。 然后把它们改写成“余数等于”的形式 然后把它们“倒回去” 求得 x=-7,y=...
扩展欧几里德定理(Extended Euclidean algorithm, EXGCD),常用于求 a x + b y = gcd ( a , b ) ax+by=\gcd(a,b) ax+by=gcd(a,b) 的一组可行解。证明设a x 1 + b y 1 = gcd ( a , b ) ax_1+by_1=\gcd(a,b) ax1+by1=gcd(a,b)...
* simplified from the above extendedGCD(m,n) * @see also "http://en.wikipedia.org/wiki/Extended_Euclidean_algorithm" * @param m * @param n * @return {d,x,y} for: d = m.x + n.y; */ publicstaticint[] extendedGCD2(intm,intn){ m = (m<0)?-m:m; n = (n<0)?-n:n;...
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=...
Euclidean algorithm, procedure for finding the greatest common divisor (GCD) of two numbers, described by the Greek mathematician Euclid in his Elements (c. 300 bc). The method is computationally efficient and, with minor modifications, is still used by computers. The algorithm involves successively...
The extended Euclidean algorithm is applied bygcdto compute unique polynomialss,tandginxsuch that s*A + t*B = g wheregis the monic greatest common divisor ofAandB. The results computed satisfy degree(s) < degree(B/g) and degree(t) < degree(A/g). The greatest common divisorgis returne...
Algorithms g = gcd(A,B) is calculated using the Euclidean algorithm.[1] [g,u,v] = gcd(A,B) is calculated using the extended Euclidean algorithm.[1] References [1] Knuth, D. “Algorithms A and X.” The Art of Computer Programming, Vol. 2, Section 4.5.2. Reading, MA: Addison-...
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) 第八节Congruences (mod p^...
The key to execute the extended Euclidean algorithm in O(nlog2n)O(nlog2n) is to be able to switch between the two representations. Conversion of [a0(x);a1(x),…,ak(x)][a0(x);a1(x),…,ak(x)] to pkpk, qkqk and rkrk The recurrence pi=pi−2+aipi−1pi=pi−2+aipi...
Extended Euclid AlgorithmWrite a JavaScript function to calculate the extended Euclid Algorithm or extended GCD.In mathematics, the Euclidean algorithm[a], or Euclid's algorithm, is an efficient method for computing the greatest common divisor (GCD) of two numbers, the largest number that divides ...