extended Euclidean algorithm
[ɪkˈstɛndɪd juːˌklɪdiən ˈælɡərɪðəm]
nounpl: extended Euclidean algorithms
algoritmo euclidiano estendido
1. A computational algorithm that extends the Euclidean algorithm to find the greatest common divisor (GCD) of two integers and also compute the Bézout coefficients, which are integers x and y that satisfy the equation ax + by = gcd(a,b)
The extended Euclidean algorithm is used in cryptography to find modular multiplicative inverses.
O algoritmo euclidiano estendido é usado em criptografia para encontrar inversos multiplicativos modulares.
2. A generalization of the Euclidean algorithm that computes additional information beyond just the GCD, specifically the coefficients of a linear Diophantine equation
Using the extended Euclidean algorithm, we can solve for integers that satisfy 3x + 5y = 1.
Usando o algoritmo euclidiano estendido, podemos resolver inteiros que satisfazem 3x + 5y = 1.
This is a technical mathematical term used universally in computer science and mathematics education in both Brazil and Portugal. It is primarily found in academic and professional contexts, particularly in courses on number theory, cryptography, and algorithms. The term maintains the same meaning across all English-speaking and Portuguese-speaking countries without significant cultural variation.
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