Arithmetic & Number Theory

Modular Exponentiation

Compute (base^exp) mod m efficiently.

Formula

Formula
r = be mod m

Variables

SymbolDefinitionType & rangeUnitsRole
b base integer (ℤ) input
e exponent integer, e ≥ 0 input
m modulus integer, m ≥ 1 input

Try it yourself

Interactive calculator
Result

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