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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

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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, you can 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 you only look for $$u$$.

$$3^-1 \equiv 4 \mod 11$$ 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?

You can use the Bezout algorithm, also available on dCode.

What does invmod mean?

The keyword invmod is the abbreviation of inverse modular.