Tool to compute the modular inverse of a number. The modular multiplicative inverse of an integer N modulo m is an integer n such as the inverse of N modulo m equals n.

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Tool to compute the modular inverse of a number. The modular multiplicative inverse of an integer N modulo m is an integer n such as the inverse of N modulo m equals n.

Answers to Questions

What is the modular Inverse? (Definition)

The value of the inverse modular of \( a \) by the modulo \( n \) is the value \( u \) such as $$ u \equiv a^{-1} \pmod n \\ a u \equiv 1 \pmod n $$

How to calculate a modular inverse?

To calculate the value of the modulo inverse, use the gcd" target="_blank">extended euclidean algorithm which find solutions to the Bezout identity \( au + bv = \text{G.C.D.}(a, b) \). Here, the gcd value is known, it is 1 : \( \text{G.C.D.}(a, b) = 1 \), thus, only the value of \( u \) is needed.

dCode uses the gcd" target="_blank">Extended Euclidean algorithm for its inverse modulo N calculator and arbitrary precision functions to get results with big integers.

The keyword invmod is the abbreviation of inverse modular.

What is a multiplicative inverse?

A multiplicative inverse is the other name of a modular inverse.

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