Unlock Modular Inverses with Ease
Discover the modular multiplicative inverse using our interactive calculator. Enter your numbers and explore the magic of modular arithmetic!
Modular Inverse Calculator
Result:
Modular Inverse:
Visualization
The modular inverse of modulo is . This is because:
What is a Modular Inverse?
In modular arithmetic, the modular multiplicative inverse of an integer 'a' modulo 'm' is an integer 'x' such that the product a*x is congruent to 1 modulo 'm'. In simpler terms, it's a number 'x' which when multiplied by 'a' gives a remainder of 1 when divided by 'm'.
Formula: a * x ≡ 1 (mod m)
Example: The modular inverse of 7 modulo 10 is 3, because (7 * 3) mod 10 = 21 mod 10 = 1.
Use Cases: Modular inverses are crucial in cryptography (like RSA), computer science, and various branches of mathematics for solving equations in modular arithmetic and performing division in modular systems. They are essential for operations where division is needed in modular arithmetic, as direct division is not always defined.