Modular Arithmetic Calculator
Perform modular arithmetic operations including addition, multiplication, exponentiation, and modular inverse calculations.
Select an operation and enter the values to perform modular arithmetic.
Ergebnisse
Geben Sie Werte ein und klicken Sie auf Berechnen, um das Ergebnis zu sehen.
Theory & Formula
Modular Arithmetic Theory
Modular arithmetic is a system of arithmetic for integers where numbers "wrap around" upon reaching a certain value (the modulus). We write a ≡ b (mod m) to mean that a and b have the same remainder when divided by m.
Basic Operations
Applications
Modular arithmetic is fundamental in cryptography (RSA, Diffie-Hellman), computer science (hash functions, checksums), and number theory. The modular inverse is used extensively in cryptographic algorithms.
Example
17 + 8 ≡ 0 (mod 5) because 25 mod 5 = 0. Also, 3^(-1) ≡ 2 (mod 5) because 3 × 2 = 6 ≡ 1 (mod 5).