Extended Euclidean Algorithm 1.1
Free Version
Publisher Description
The Euclidean algorithm is usually used simply to find the greatest common divisor of two integers. (For a description of this algorithm, see the notes about additional topics in number theory.) The standard Euclidean algorithm gives the greatest common divisor and nothing else. However, if we keep track of a bit more information as we go through the algorithm, we can discover how to write the greatest common divisor as an integer linear combination of the two original numbers. In other words, we can find integers s and t such that
gcd(a, b) = sa + tb.
[Note that, since gcd(a, b) is usually less than both a and b, one of s or t will usually be negative.]
As a reminder, here are the steps of the standard Euclidean algorithm to find the greatest common divisor of two positive integers a and b:
Set the value of the variable c to the larger of the two values a and b, and set d to the smaller of a and b.
Find the remainder when c is divided by d. Call this remainder r.
If r = 0, then gcd(a, b) = d. Stop.
Otherwise, use the current values of d and r as the new values of c and d, respectively, and go back to step 2.
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 our way through an example to illustrate the main ideas.
About Extended Euclidean Algorithm
Extended Euclidean Algorithm is a free app for Android published in the Teaching & Training Tools list of apps, part of Education.
The company that develops Extended Euclidean Algorithm is gokhanku. The latest version released by its developer is 1.1.
To install Extended Euclidean Algorithm on your Android device, just click the green Continue To App button above to start the installation process. The app is listed on our website since 2016-05-02 and was downloaded 6 times. We have already checked if the download link is safe, however for your own protection we recommend that you scan the downloaded app with your antivirus. Your antivirus may detect the Extended Euclidean Algorithm as malware as malware if the download link to com.gokhankurt.extendedeuclid is broken.
How to install Extended Euclidean Algorithm on your Android device:
- Click on the Continue To App button on our website. This will redirect you to Google Play.
- Once the Extended Euclidean Algorithm is shown in the Google Play listing of your Android device, you can start its download and installation. Tap on the Install button located below the search bar and to the right of the app icon.
- A pop-up window with the permissions required by Extended Euclidean Algorithm will be shown. Click on Accept to continue the process.
- Extended Euclidean Algorithm will be downloaded onto your device, displaying a progress. Once the download completes, the installation will start and you'll get a notification after the installation is finished.
