Power Mod Calculator
Free Power mod Calculator for arithmetic. Enter values to get step-by-step solutions with formulas and graphs. See charts, tables, and visual results.
Reviewed by Manoj Kumar, Mathematics Educator
Formula
b^e mod m (computed via repeated squaring)
Modular exponentiation computes base^exponent mod modulus efficiently by converting the exponent to binary and performing at most 2*log2(exponent) modular multiplications. At each step, the intermediate result is reduced modulo m, keeping all numbers manageable.
Worked Examples
Example 1: RSA-Style Computation
Problem:Compute 7^13 mod 11 using the repeated squaring method.
Solution:13 in binary = 1101\nStep 1: bit 0 is 1, result = 1 * 7 = 7 mod 11 = 7, square: 7^2 = 49 mod 11 = 5\nStep 2: bit 1 is 0, skip multiply, square: 5^2 = 25 mod 11 = 3\nStep 3: bit 2 is 1, result = 7 * 3 = 21 mod 11 = 10, square: 3^2 = 9 mod 11 = 9\nStep 4: bit 3 is 1, result = 10 * 9 = 90 mod 11 = 2\n\nVerification: 7^13 = 96889010407 mod 11 = 2
Result:7^13 mod 11 = 2
Example 2: Large Exponent with Euler Reduction
Problem:Compute 3^1000 mod 7 using Euler theorem.
Solution:phi(7) = 6 (since 7 is prime)\nBy Euler theorem: 3^6 mod 7 = 1\nReduce exponent: 1000 mod 6 = 4\nSo 3^1000 mod 7 = 3^4 mod 7\n3^4 = 81\n81 mod 7 = 81 - 11*7 = 81 - 77 = 4
Result:3^1000 mod 7 = 4 (reduced exponent from 1000 to 4)
References
Reviewed by Manoj Kumar, Mathematics Educator · Editorial policy