The above is an application of congruence article in the chapter on theory of numbers in Higher Algebra By H. Hall and S. Knight May pdf probably available online. Sign up to join this community. The best answers are voted up and rise to the top. Stack Overflow for Teams — Collaborate and share knowledge with a private group. Create a free Team What is Teams? Learn more. Ask Question. Asked 10 years, 8 months ago. Active 10 months ago. Viewed k times. Cooperation 2 2 silver badges 14 14 bronze badges.
Chan Chan Add a comment. Active Oldest Votes. Below is the implementation of this method. Since we know that a and m are relatively prime, we can put value of gcd as 1. Python3 Python3 program to find modular inverse of a under modulo m This program works only if m is prime. Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above. Skip to content. Change Language. Related Articles. Table of Contents.
Save Article. Improve Article. Now, let's see how it's connected to the multiplicative modular inverse. Applying the mod m operation to both sides of the above equation, we obtain:.
As a result, we can simplify our equation to:. But hey, this last equation says that the integer x found by the extended Euclid algorithm is precisely the multiplicative inverse of a modulo m!
We assume that m is a prime number and a is not a multiplicity of m. Embed Share via. Table of contents: Modulo congruence What is inverse modulo? How to find the modular inverse? How to use this inverse modulo calculator? Modulo congruence Before we learn what inverse modulo is, we need to get familiar with the congruence relation.
Let's take a look at two examples. Example 1. We are ready to learn what the inverse modulo is! What is inverse modulo?
Let's talk more about these two notions: Modular additive inverse In the case of addition, the identity element is 0. Here are the steps you can follow to find the additive modular inverse of a modulo m : Write down -a.
Write down the numbers created by repeatedly adding or subtracting m to a. Pick the number that falls between 0 and m - 1. Let's see how it works. How familiar are you with modular arithmetic?
It is a fact from group theory that only one of these numbers should be the inverse. Notation-wise, what I've written above is non-standard. Sign up to join this community.
The best answers are voted up and rise to the top. Stack Overflow for Teams — Collaborate and share knowledge with a private group. Create a free Team What is Teams? Learn more. Ask Question. Asked 6 years, 3 months ago. Active 3 years, 3 months ago.
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