Modular Exponentiation 5^19mod23

Enter Modular Exponentiation

Solve 519 mod 23 using:

Modular exponentiation

Build an algorithm:

n is our exponent = 19

y = 1 and u ≡ 5 mod 23 = 5

See here

n = 19 is odd

Since 19 is odd, calculate (y)(u) mod p

(y)(u) mod p = (1)(5) mod 23

(y)(u) mod p = 5 mod 23

5 mod 23 = 5
Reset y to this value

Determine u2 mod p

u2 mod p = 52 mod 23

u2 mod p = 25 mod 23

25 mod 23 = 2
Reset u to this value

Cut n in half and take the integer

19 ÷ 2 = 9

n = 9 is odd

Since 9 is odd, calculate (y)(u) mod p

(y)(u) mod p = (5)(2) mod 23

(y)(u) mod p = 10 mod 23

10 mod 23 = 10
Reset y to this value

Determine u2 mod p

u2 mod p = 22 mod 23

u2 mod p = 4 mod 23

4 mod 23 = 4
Reset u to this value

Cut n in half and take the integer

9 ÷ 2 = 4

n = 4 is even

Since 4 is even, we keep y = 10

Determine u2 mod p

u2 mod p = 42 mod 23

u2 mod p = 16 mod 23

16 mod 23 = 16
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 = 10

Determine u2 mod p

u2 mod p = 162 mod 23

u2 mod p = 256 mod 23

256 mod 23 = 3
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 = (10)(3) mod 23

(y)(u) mod p = 30 mod 23

30 mod 23 = 7
Reset y to this value

Determine u2 mod p

u2 mod p = 32 mod 23

u2 mod p = 9 mod 23

9 mod 23 = 9
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

519 mod 23 ≡ 7

You have 1 free calculations remaining

What is the Answer?

519 mod 23 ≡ 7

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

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