Multiplicative Inverse Modulo Calculator

A multiplicative inverse modulo calculator is a tool to find the multiplicative inverse of a number under a given modulus.

In modular arithmetic, the multiplicative inverse of an integer 'a' is another integer 'x' such that (a * x) ≡ 1 (mod m). This calculator simplifies the process, making it faster and more accurate.

Given below is a step-by-step process on how to use the calculator:

Step 1: Enter the integer and modulus: Input the integer and the modulus into the given fields.

Step 2: Click on calculate: Click on the calculate button to find the inverse.

Step 3: View the result: The calculator will display the result instantly.

To calculate the multiplicative inverse of a number 'a' under modulus 'm', you need to find an integer 'x' such that: (a * x) ≡ 1 (mod m)

This can be found using the Extended Euclidean Algorithm, which can efficiently compute the inverse when 'a' and 'm' are coprime.

When using a multiplicative inverse modulo calculator, here are a few tips and tricks to help avoid common mistakes:

• Ensure the integer and modulus are coprime; otherwise, an inverse does not exist.
   
• Understand that not all numbers have an inverse under a modulus.
   
• Use the calculator to verify manual calculations if needed.

• Multiplicative Inverse: An integer 'x' such that (a * x) ≡ 1 (mod m).

• Coprime: Two numbers with no common divisors other than 1.

• Modulus: The divisor in modular arithmetic, denoted as 'm' in (a * x) ≡ 1 (mod m).

• Extended Euclidean Algorithm: A method for finding the inverse of a number in modular arithmetic.

• Modulo Operation: An operation that finds the remainder when one integer is divided by another.