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 $(210,65)$ number-theory

Apr 9, 2021 · I am learning about the Euclidean algorithm, and here is an image with the workings. I got stuck towards the end. My friend tried to help me, saying just put the three together. I understand that on the second line the equation is rearranged, however I do not understand how we got to the third line: 3 - 1*26 + 8*3 = 3 + 8*3 - 1*26 = (1+8)*3 - 1*26

Jul 10, 2019 · $\begingroup$ Euclid's algorithm is much less computationally complex. Prime decomposition is a difficult computational problem for reasonably large numbers, and Euclid's algorithm is a lot of times just one of the many steps that you have to perform for checking each of the candidates. $\endgroup$ –

Jun 11, 2017 · I am guessing that you might also have a problem with obtaining the particular solution from Euclid's Algorithm: Well the way we do it as follows- Say we have the LDE $$18x+189y=81$$ and we would like to obtain a particular …

Nov 29, 2019 · So you still get decreasing sequences of positive integers, and so the argument still applies. And at any rate, I don't think that what you say is a real reason to complain of incompleteness in the answer, since Euclid's algorithm is an algorithm for finding the gcd of a pair of integers. $\qquad$ $\endgroup$ –

Use Euclid's Algorithm on $13$ and $35$, the same way as for finding $\gcd(13,35)$.

I've been struggling with a basic exercise involving Euclid's algorithm and mathematical induction. Given the following definition of the Euclid's algorithm (in Java): int gcd(int a, int b) { ...

Sep 3, 2020 · I saw this Khan Academy video on the visualization of Euclid's algorithm. The problem was to find the HCF of $32$ and $12$. At $6:53$, the instructor reduced the original problem to $12$ and $8$ ...

Oct 3, 2019 · The GCD algorithm comes from two principles, the division algorithm and that given any two integers with a common factor, their sum and difference are both divisible by that common factor. Suppose you have two natural numbers x and y each divisible by q. Then x=aq and y=bq for some natural numbers a and b. x+y = q(a+b), so is divisible by q.

Is Euclid's algorithm for the GCD of two numbers wrong? 2. $15x\equiv 20 \pmod{88}$ Euclid's algorithm. 1.