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Modular Exponentiation 3^5Mod11

Chloe Bennett • • 2 min read
Modular Exponentiation 3^5Mod11
Modular Exponentiation 3^5mod11

Enter Modular Exponentiation

Solve 35 mod 11 using:

Modular exponentiation

Build an algorithm:

n is our exponent = 5

y = 1 and u ≡ 3 mod 11 = 3

See here

n = 5 is odd

Since 5 is odd, calculate (y)(u) mod p

(y)(u) mod p = (1)(3) mod 11

(y)(u) mod p = 3 mod 11

3 mod 11 = 3
Reset y to this value

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

5 ÷ 2 = 2

n = 2 is even

Since 2 is even, we keep y = 3

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

2 ÷ 2 = 1

n = 1 is odd

Since 1 is odd, calculate (y)(u) mod p

(y)(u) mod p = (3)(4) mod 11

(y)(u) mod p = 12 mod 11

12 mod 11 = 1
Reset y to this value

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

1 ÷ 2 = 0

Because n = 0, we stop

We have our answer

Final Answer

35 mod 11 ≡ 1


What is the Answer?

35 mod 11 ≡ 1

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?

Successive Squaring I = number of digits in binary form of n. Run this many loops of a2 mod p

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

Chloe Bennett
Author

Chloe Bennett

Chloe Bennett explores the intersection of pop culture, streaming entertainment, digital trends, and contemporary lifestyle. Her weekly commentary reaches thousands of culture enthusiasts.