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.
Modular Multiplicative Inverse - dCode
Tag(s) : Arithmetics
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Modular Multiplicative Inverse
Modular Inverse Calculator
Batch InvMod Calculator
Answers to Questions (FAQ)
What is the modular Inverse? (Definition)
The value of the modular inverse of $ a $ by the modulo $ n $ is the value $ a^{-1} $ such that $ a \cdot a^{-1} \equiv 1 \pmod n $
It is common to note this modular inverse $ u $ and to use these equations $$ u \equiv a^{-1} \pmod n \\ a u \equiv 1 \pmod n $$
If a modular inverse exists then it is unique.
How to calculate a modular inverse?
To calculate the value of the modulo inverse, use the extended euclidean algorithm which finds 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.
Example: $ 3^{-1} \equiv 4 \mod 11 $ because $ 4 \times 3 = 12 $ and $ 12 \equiv 1 \mod 11 $
dCode uses the Extended Euclidean algorithm for its inverse modulo N calculator and arbitrary precision functions to get results with big integers.
How to calculate v in au+bv?
Use the Bezout identity, also available on dCode.
What does invmod mean?
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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