Modular Exponentiation 3^8Mod11
Enter Modular Exponentiationsolve 38 Mod 11 Using: Modular exponentiationBuild an Algorithm: N Is Our Exponent = 8Y = 1 and U ≡ 3 Mod 11 = 3See Heren = 8 Is...
Enter Modular Exponentiation
Solve 38 mod 11 using:
Modular exponentiation
Build an algorithm:
n is our exponent = 8
y = 1 and u ≡ 3 mod 11 = 3
See here
n = 8 is even
Since 8 is even, we keep y = 1
Determine u2 mod p
u2 mod p = 32 mod 11
u2 mod p = 9 mod 11
9 mod 11 = 9
Reset u to this value
Cut n in half and take the integer
8 ÷ 2 = 4
n = 4 is even
Since 4 is even, we keep y = 1
Determine u2 mod p
u2 mod p = 92 mod 11
u2 mod p = 81 mod 11
81 mod 11 = 4
Reset u to this value
Cut n in half and take the integer
4 ÷ 2 = 2
n = 2 is even
Since 2 is even, we keep y = 1
Determine u2 mod p
u2 mod p = 42 mod 11
u2 mod p = 16 mod 11
16 mod 11 = 5
Reset u to this value
Cut n in half and take the integer
2 ÷ 2 = 1
n = 1 is odd
Since 1 is odd, calculate (y)(u) mod p
(y)(u) mod p = (1)(5) mod 11
(y)(u) mod p = 5 mod 11
5 mod 11 = 5
Reset y to this value
Determine u2 mod p
u2 mod p = 52 mod 11
u2 mod p = 25 mod 11
25 mod 11 = 3
Reset u to this value
Cut n in half and take the integer
1 ÷ 2 = 0
Because n = 0, we stop
We have our answer
Final Answer
38 mod 11 ≡ 5
What is the Answer?
38 mod 11 ≡ 5
How does the Modular Exponentiation and Successive Squaring Calculator work?
Free Modular Exponentiation and Successive Squaring Calculator - Solves xn mod p using the following methods:
* Modular Exponentiation
* Successive Squaring
This calculator has 1 input.
What 1 formula is used for the Modular Exponentiation and Successive Squaring Calculator?
For more math formulas, check out our Formula Dossier
What 6 concepts are covered in the Modular Exponentiation and Successive Squaring Calculator?
- exponent
- The power to raise a number
- integer
- a whole number; a number that is not a fraction
...,-5,-4,-3,-2,-1,0,1,2,3,4,5,... - modular exponentiation
- the remainder when an integer b (the base) is raised to the power e (the exponent), and divided by a positive integer m (the modulus)
- modulus
- the remainder of a division, after one number is divided by another.
a mod b - remainder
- The portion of a division operation leftover after dividing two integers
- successive squaring
- an algorithm to compute in a finite field
Example calculations for the Modular Exponentiation and Successive Squaring Calculator
David Miller brings 15 years of experience in global economics, personal finance strategy, and market dynamics. He specializes in turning complex economic trends into actionable insights for everyday readers.
