Problem 1750. Modular multiplicative inverse

Created by Mehmet OZC

Solve Later

Modular multiplicative inverse is used for The Chinese Remainder Theorem and RSA algorithm. You can visit Wikipedia.

Normal Modulus

X = M (mod Y)

You can solve that with M = mod(X,Y)

Inverse Modulus

X.B = M (mod Y)

given X,M,Y calculate B

B = inverse_modulus(X,M,Y)

Solve

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Last Solution submitted on Jun 17, 2025

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Rafael S.T. Vieira on 12 Oct 2020

The inverse modulus would be to find X such that mod(X,Y) = M where M and Y are known (or X === M (mod Y)); this is the chinese remainder theorem which is generalized for any number of Y's and M's when all have the same X and the GCD of all Y = 1 (greatest common divisor). The author is actually requesting Y*Z + M = X*B, which is not the same thing, or the inverse modulus.

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Problem 1750. Modular multiplicative inverse

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Problem 1750. Modular multiplicative inverse

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Last 200 Solutions

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