Unlock the power of modular arithmetic with our Multiplicative Inverse Modulo Calculator. Quickly find the integer 'x' such that (a * x) ≡ 1 (mod n), essential for cryptography and number theory. Simply input your values for 'a' and 'n' to get instant results!
Formula:
The multiplicative inverse of 'a' modulo 'n', denoted as a-1 (mod n), is an integer 'x' such that:
(a * x) ≡ 1 (mod n)
Where:
- a: The integer for which to find the inverse.
- x: The multiplicative inverse.
- n: The modulus.
An inverse exists only if 'a' and 'n' are coprime (i.e., their greatest common divisor, GCD, is 1).