The Extended Euclidean Algorithm Explained step-by-step with examples. Before you read this page Make sure that you have read the page about the Euclidean Algorithm (or watch the video instead). …

Extended Euclidean Algorithm The extended Euclidean algorithm is an algorithm to compute integers x x and y y such that a x + b y = gcd (a, b) ax +by = gcd(a,b) given a a and b b. The existence of such …

Feb 26, 2010 · The extended Euclidean algorithm uses the same framework, but there is a bit more bookkeeping. Before we present a formal description of the extended Euclidean algorithm, let’s work …

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

Feb 17, 2025 · The extended Euclidean algorithm is particularly useful when a and b are coprime (or gcd is 1). Since x is the modular multiplicative inverse of "a modulo b", and y is the modular multiplicative …

Example of Extended Euclidean Algorithm Recall 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:

The Extended Euclidean Algorithm will tell us how to nd x and y. Rather than give a set of equations, we'll show how it works with the two examples we calclated in Section 3.1.3.

Learn the Extended Euclidean Algorithm step by step and discover how it is used to compute the modular multiplicative inverse, with detailed examples, diagrams, and Python code.

Oct 12, 2025 · This implementation of extended Euclidean algorithm produces correct results for negative integers as well. Iterative version It's also possible to write the Extended Euclidean …

The extended Euclidean algorithm can only be applied if \ ( \text {GCD} (a,b) \) divides the constant term \ ( c \) in the Diophantine equation. For example, consider: