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This tutorial shows how to find the inverse of a number when dealing with a modulus. When dealing with modular arithmetic, numbers can only be represented as.

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• For the basics and the table notation. Extended Euclidean Algorithm. Unless you only want to use this calculator for the basic Euclidean Algorithm. Modular multiplicative inverse. in case you are interested in calculating the modular multiplicative inverse of a number modulo n. using the Extended Euclidean Algorithm.
• 11. Modular Multiplicative Inverse Given two integers 'a' and 'm'. The task is to find the smallest modular multiplicative inverse of 'a' under modulo 'm'. Example 1: Input: a = 3 m = 11 Output: 4 Explanation: Since (4*3) mod 11 = 1, 4 is modulo inverse of 3. One might think, 15 also as a valid output as " (15*3) mod 11" is also ...
• E.g., 2 is the multiplicative inverse of 3 modulo 5; and 3 is the multiplicative inverse of 2 modulo 5. ...
• Here we check if the gcd is 1 or not. If 1, it suggests that m isn't prime. So, in this case, the inverse doesn't exist. a = 3; m = 11 mod_Inv (a,m) output: Modular multiplicative inverse is 4. This is how we can calculate modular multiplicative inverse using Fermat's little theorem. The reason we have used this method is the time factor.
• On Newton-Raphson iteration for multiplicative inverses modulo prime powers by Dumas (2012). Jeff Hurchalla wrote a paper on it: Speeding up the Integer Multicative Inverse. Credit: Marc Reynolds asked on Twitter for an informal reference on computing the multiplicative inverse modulo a power of two. It motivated me to write this blog post.