How this calculation works
Verify the result by multiplying it by the input and reducing the product modulo the chosen modulus.
THE FORMULA
ax ≡ 1 (mod m)A worked example
7 × 15 = 105, which leaves remainder 1 modulo 26.
Good to know
An inverse exists exactly when the input and modulus are coprime.
Reference: NIST DLMF, Functions of Number Theory (opens in a new tab) ↗
Read the result
Find the multiplicative inverse modulo an integer using Bézout coefficients.
The primary result is labeled “Least nonnegative inverse”. Keep the input definitions in view when comparing this result with another method.
Try a related calculation
An inverse exists exactly when the input and modulus are coprime.
For a related exercise, try the greatest common divisor.
A few questions, answered
How can I check the default inputs by hand?
7 × 15 = 105, which leaves remainder 1 modulo 26.
Which rule does this calculator apply?
ax ≡ 1 (mod m)