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Modular Multiplicative Inverse

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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Modular Multiplicative Inverse -

Tag(s) : Mathematics, Arithmetics

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# Modular Multiplicative Inverse

## Modular Inverse Calculator

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.

### What is the modular Inverse?

The value of the inverse modular of $$a$$ by the modulus $$n$$ 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 modular inverse, use the extended euclide algorithm which find solutions to the identity of Bezout $$au + bv = \text{G.C.D.}(a, b)$$ except that here $$\text{G.C.D.}(a, b) = 1$$ and look for $$u$$.

Example: $$3^-1 \equiv 4 \mod 11$$ because $$4 \times 3 = 12$$ and $$12 \equiv 1 \mod 11$$

dCode uses the Extended Euclidian algorithm and arbitrary precision functions to get resulsts with bg integers.

### How to calculate v?

Use the Bezout algorithm, also available on dCode.

### What does invmod mean?

The keyword invmod is the abbreviation of inverse modular.