Inverse Modulo Calculator (Modular Multiplicative Inverse)

Welcome to the world of inverse modulo! In this article, we’ll demystify this mathematical concept and equip you with the knowledge and tools to calculate inverse modulo effortlessly. Whether you’re a student grappling with number theory or a curious mind exploring mathematical wonders, we’ve got you covered!

Inverse Modulo Calculator

a * x ≡ 1 (mod m)

Eg, what is inverse of 2 modulo 9? Enter 2 in the first input box and enter 9 in the second input box, then click Calculate button.

Calculate Reset

What is the Inverse Modulo

Inverse modulo, also known as modular multiplicative inverse, is a crucial concept in number theory. It involves finding a number that, when multiplied with a given number modulo a specific modulus, yields a remainder of 1. The inverse modulo of ‘a‘ modulo ‘m‘ is represented as ‘a^-1 mod m‘. In simple terms, it’s the number that, when multiplied with ‘a‘ and then divided by ‘m‘, gives a remainder of 1.

The formula for finding the inverse modulo is:

a^-1 mod m ≡ x

where a * x ≡ 1 (mod m)

How to Calculate the Inverse Modulo

To calculate the inverse modulo, follow these steps:

Step 1: Find the value of ‘a‘ and ‘m‘.
Step 2: Use the extended Euclidean algorithm to determine ‘x‘, such that a * x ≡ 1 (mod m).
Step 3: The value of ‘x‘ will be the inverse modulo of ‘a‘ modulo ‘m‘.

Let’s take an example to illustrate the process:

Find the inverse modulo of 5 modulo 11.

Step 1: a = 5, m = 11

Step 2: Using the extended Euclidean algorithm, we find x = 9, as 5 * 9 ≡ 1 (mod 11).

Step 3: The inverse modulo of 5 modulo 11 is 9, represented as 5^-1 mod 11 ≡ 9.

What is an Inverse Modulo Calculator

Introducing our powerful Inverse Modulo Calculator – your trusty assistant in number crunching! Our calculator is designed to help you effortlessly find the inverse modulo of any number modulo any modulus. Whether you’re a student, a professional, or an enthusiast, our calculator is here to simplify your mathematical endeavors.

How to use the modulo calculator

Using our Inverse Modulo Calculator is as easy as 1, 2, 3! Follow these simple steps:

1Enter the value of 'a' (the number whose inverse modulo you want to find)
2Enter the value of 'm' (the modulus).
3Click Calculate button to calculate the modulo of 'a' modulo 'm', or click Reset button to start a new calculation.

FAQs

Q: What is the purpose of inverse modulo?
A: Inverse modulo is used to find the number that, when multiplied with a given number modulo a specific modulus, yields a remainder of 1. It has various applications in cryptography, computer science, and number theory.

Q: Are there any numbers without an inverse modulo?
A: Yes, not all numbers have an inverse modulo. A number ‘a‘ has an inverse modulo ‘m‘ only if ‘a‘ and ‘m‘ are coprime (i.e., their greatest common divisor is 1).

Q: Can inverse modulo be negative?
A: Yes, the inverse modulo can be negative if the given number ‘a‘ is negative.

Q: What applications does inverse modulo have in cryptography?
A: Inverse modulo is fundamental in public-key cryptography algorithms like RSA. It is used to encrypt and decrypt data securely.

Q: How is inverse modulo related to modular arithmetic?
A: Inverse modulo is a significant concept in modular arithmetic. It helps find the multiplicative inverse of a number modulo a specific modulus.

Q: How does the calculator deal with non-integer inputs?
A: The calculator accepts and processes only integer inputs for both the number and modulus.

Conclusion

Congratulations! You’ve unlocked the secrets of inverse modulo and harnessed the power of our Inverse Modulo Calculator. Armed with this knowledge, you can confidently tackle complex mathematical problems and appreciate the beauty of number theory. So go forth, explore, and embrace the wonders of inverse modulo with newfound enthusiasm!

Inverse Modulo Calculator (Modular Multiplicative Inverse)