arithmetic and computer programming, the extended Euclidean algorithm is an extension to the Euclidean algorithm, and computes, in addition to the greatest...

In mathematics, the Euclidean algorithm, or Euclid's algorithm, is an efficient method for computing the greatest common divisor (GCD) of two integers...

The binary GCD algorithm, also known as Stein's algorithm or the binary Euclidean algorithm, is an algorithm that computes the greatest common divisor...

ring of integers), but lacks an analogue of the Euclidean algorithm and extended Euclidean algorithm to compute greatest common divisors. So, given an...

RSA algorithm. A benefit for the computer implementation of these applications is that there exists a very fast algorithm (the extended Euclidean algorithm)...

{n}}} . Solutions to this equation are easily obtained using the extended Euclidean algorithm. To find the needed a {\displaystyle a} , b {\displaystyle b}...

Sugiyama's adaptation of the Extended Euclidean algorithm. Correction of unreadable characters could be incorporated to the algorithm easily as well. Let k 1...

a quotient and a remainder Euclidean algorithm, a method for finding greatest common divisors Extended Euclidean algorithm, a method for solving the Diophantine...

unique. A pair of Bézout coefficients can be computed by the extended Euclidean algorithm, and this pair is, in the case of integers one of the two pairs...

Lehmer's GCD algorithm, named after Derrick Henry Lehmer, is a fast GCD algorithm, an improvement on the simpler but slower Euclidean algorithm. It is mainly...

identity. Numbers p and q like this can be computed with the extended Euclidean algorithm. gcd(a, 0) = |a|, for a ≠ 0, since any number is a divisor of...

m_{1}} and m 2 {\displaystyle m_{2}} may be computed by the extended Euclidean algorithm. A solution is given by x = a 1 m 2 n 2 + a 2 m 1 n 1 . {\displaystyle...

are coprime. It can be constructed using the extended Euclidean algorithm. The extended Euclidean algorithm efficiently determines integers R′ and N′ that...

deterministic algorithm and within ( 33 + ε ) / 25 {\displaystyle (33+\varepsilon )/25} by a randomized algorithm. The TSP, in particular the Euclidean variant...

computed before the message is known. It may be computed using the extended Euclidean algorithm or using Fermat's little theorem as k q − 2 mod q {\displaystyle...

de ≡ 1 (mod λ(n)); d can be computed efficiently by using the extended Euclidean algorithm, since, thanks to e and λ(n) being coprime, said equation is...

the modular multiplicative inverse d of b modulo m using the extended Euclidean algorithm. That is: c = be mod m = d−e mod m, where e < 0 and b ⋅ d ≡ 1...

decoding algorithm. In 1975, another improved BCH scheme decoder was developed by Yasuo Sugiyama, based on the extended Euclidean algorithm. In 1977,...

{p}}\\m_{q}&=c^{{\frac {1}{4}}(q+1)}{\bmod {q}}\end{aligned}}} Use the extended Euclidean algorithm to find y p {\displaystyle y_{p}} and y q {\displaystyle y_{q}}...

Kuṭṭaka algorithm has much similarity with and can be considered as a precursor of the modern day extended Euclidean algorithm. The latter algorithm is a...

multiplication by the inverse modulo p, which may be computed using the extended Euclidean algorithm. A particular case is GF(2), where addition is exclusive OR (XOR)...

are called integer division algorithms, the best known of which being long division. Euclidean division, and algorithms to compute it, are fundamental...

of an element may be computed by using the extended Euclidean algorithm (see Extended Euclidean algorithm § Modular integers).[citation needed] Let F...

divergent series. One way to compute a Padé approximant is via the extended Euclidean algorithm for the polynomial greatest common divisor. The relation R (...

Some polynomial Diophantine equations can be solved using the extended Euclidean algorithm, which works as well with polynomials as it does with integers...

exponential extended binary tree extended Euclidean algorithm extended k-d tree extendible hashing external index external memory algorithm external memory...

the modular multiplicative inverse can be computed using the extended Euclidean algorithm. An alternative is to compute s − 1 {\displaystyle s^{-1}} as...

Pollard's rho algorithm for logarithms Pohlig–Hellman algorithm Euclidean algorithm: computes the greatest common divisor Extended Euclidean algorithm: also solves...

fraction can be converted into an equivalent whole number using the extended Euclidean algorithm. This conversion can be used to perform modular division: dividing...

means congruence modulo p {\displaystyle p} in the integers. The extended Euclidean algorithm finds k {\displaystyle k} quickly. With Diffie–Hellman, a cyclic...