Arithmetic & Number Theory
Modular Exponentiation
Compute (base^exp) mod m efficiently.
Formula
Formula
r = be mod m
Variables
| Symbol | Definition | Type & range | Units | Role |
|---|---|---|---|---|
| b | base | integer (ℤ) | — | input |
| e | exponent | integer, e ≥ 0 | — | input |
| m | modulus | integer, m ≥ 1 | — | input |
Try it yourself
Interactive calculator
Worked examples
Example 1
Givenbase b = 7, exponent e = 256, modulus m = 13
Result9
Example 2
Givenbase b = 2, exponent e = 10, modulus m = 1000
Result24