Extended Euclid's Algorithm
Explore Extended Euclid's algorithm to solve linear Diophantine equations of the form Ax + By = gcd(A, B). Understand how to compute coefficients x and y using recursion and the Euclidean method, and implement this efficiently in C++ with step-by-step explanations.
We'll cover the following...
We'll cover the following...
What is the Extended Euclid’s algorithm?
The Extended Euclid’s algorithm is used to find the solution of equations of the form Ax + By = C , where C is a
multiple of divisor of A and B, or in other words C = gcd(A, B). Extended Euclid’s works in the same manner as the Euclid’s algorithm.
Let the equation be Ax + By = 1 (let the solutions of this equation be x’ and y’). We have been given that gcd(A, B) is 1, then
the solutions of equation Ax + By = k where k is a multiple ...