🔄Modular Arithmetic Calculator

Perform modulo operations and explore modular arithmetic concepts.

modulus (n)

Result

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About Modular Arithmetic Calculator

Calculate modulo operations (a mod n), modular inverse, modular exponentiation, and check congruences. A clean, step-by-step tool for understanding modular arithmetic used in cryptography, computer science, and number theory.

How to Use Modular Arithmetic Calculator

1
Choose the operation
Select modulo, modular inverse, modular exponentiation, or congruence check.
2
Enter the values
Input the operands (a, b, modulus n) for the selected operation.
3
View the result
The answer is displayed with the calculation steps for learning and verification.

Common Use Cases

Solving modular arithmetic problems in maths courses
Understanding the basis of RSA and cryptographic algorithms
Computing hash function modulo operations
Checking clock arithmetic and cyclic number patterns

Frequently Asked Questions

What does 'a mod n' mean?

a mod n is the remainder when a is divided by n. For example, 17 mod 5 = 2 because 17 = 3×5 + 2. In programming, this is the % operator in most languages.

What is the modular inverse?

The modular inverse of a modulo n is the number x such that (a × x) ≡ 1 (mod n). It exists only when a and n are coprime (GCD = 1). The calculator uses the extended Euclidean algorithm to find it.