Inverse Modulo Calculator
Result
About Modular Multiplicative Inverse
The modular multiplicative inverse of an integer a modulo m is an integer x such that:
(a × x) ≡ 1 (mod m)
In other words, when we multiply a by x and divide by m, the remainder is 1.
Properties:
- The inverse exists if and only if a and m are coprime (gcd(a,m) = 1)
- If the inverse exists, it is unique modulo m
- The inverse is always between 0 and m-1
Examples:
| Number (a) | Modulus (m) | Inverse (x) | Verification |
|---|---|---|---|
| 3 | 11 | 4 | 3 × 4 = 12 ≡ 1 (mod 11) |
| 5 | 12 | 5 | 5 × 5 = 25 ≡ 1 (mod 12) |
| 7 | 13 | 2 | 7 × 2 = 14 ≡ 1 (mod 13) |
Applications:
- Cryptography (RSA algorithm)
- Error detection and correction
- Solving linear congruences
- Number theory problems
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