Jul 7, 2016 · Why does the Euclidean algorithm always terminate? Can we make this effective by bounding the number of steps it takes in terms of the original integers?

Oct 3, 2019 · why the Euclidean algorithm for finding the GCD of two numbers always works by using a standard argument in number theory: showing that a problem is equivalent to the …

Sep 1, 2016 · Euclid's Division Algorithm is an algorithm to find the greatest common divisor ($\gcd$) of two natural numbers facilitated by repeated use of the Division Lemma until in the …

Mar 19, 2014 · What does the euclidean algorithm compute, and what problems is the extended euclidean algorithm used for? Can someone please show how they each differ on the pair …

Mar 27, 2012 · The fundamental lemma below, interpreted procedurally, yields Euclid's classical algorithm to compute the gcd using repeated subtraction. For a simple approach to the …

I already got idea of solving gcd with three numbers. But I am wondering how to solve the extended Euclidean algorithm with three, such as: 47x + 64y + 70z = 1 Could anyone give me …

Jun 11, 2017 · This arose from the OP's prior question.. As I showed there it has a one-line solution using Gauss's algorithm (here simpler than using the extended Euclidean algorithm).

Oct 18, 2017 · I want to ask two things. The first is why are consecutive Fibonacci numbers the worst case for Euclid's algorithm? I keep seeing people say it in passing and I understand that …

Oct 14, 2017 · I know how to use the extended euclidean algorithm for finding the GCD of integers but not polynomials. I can't really find any good explanations of it online. The question …

Aug 9, 2020 · I want to prove that in last step of Euclidean algorithm we have lcm representation (by last step I mean the step with zero representation as $0 = x * E_0 + y * E_1$, where we …