Modular Exponentiation 3^5mod17

Enter Modular Exponentiation

Solve 35 mod 17 using:

Modular exponentiation

Build an algorithm:

n is our exponent = 5

y = 1 and u ≡ 3 mod 17 = 3

See here

n = 5 is odd

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

(y)(u) mod p = (1)(3) mod 17

(y)(u) mod p = 3 mod 17

3 mod 17 = 3
Reset y to this value

Determine u2 mod p

u2 mod p = 32 mod 17

u2 mod p = 9 mod 17

9 mod 17 = 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 17

u2 mod p = 81 mod 17

81 mod 17 = 13
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)(13) mod 17

(y)(u) mod p = 39 mod 17

39 mod 17 = 5
Reset y to this value

Determine u2 mod p

u2 mod p = 132 mod 17

u2 mod p = 169 mod 17

169 mod 17 = 16
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 17 ≡ 5

You have 1 free calculations remaining

What is the Answer?

35 mod 17 ≡ 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?

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?

exponentThe power to raise a numberintegera whole number; a number that is not a fraction
...,-5,-4,-3,-2,-1,0,1,2,3,4,5,...modular exponentiationthe remainder when an integer b (the base) is raised to the power e (the exponent), and divided by a positive integer m (the modulus)modulusthe remainder of a division, after one number is divided by another.
a mod bremainderThe portion of a division operation leftover after dividing two integerssuccessive squaringan algorithm to compute in a finite field

Example calculations for the Modular Exponentiation and Successive Squaring Calculator

Modular Exponentiation and Successive Squaring Calculator Video

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