Enter Modular Exponentiation
Solve 319 mod 23 using:
Modular exponentiation
Build an algorithm:
n is our exponent = 19
y = 1 and u ≡ 3 mod 23 = 3
See here
n = 19 is odd
Since 19 is odd, calculate (y)(u) mod p
(y)(u) mod p = (1)(3) mod 23
(y)(u) mod p = 3 mod 23
3 mod 23 = 3
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
19 ÷ 2 = 9
n = 9 is odd
Since 9 is odd, calculate (y)(u) mod p
(y)(u) mod p = (3)(9) mod 23
(y)(u) mod p = 27 mod 23
27 mod 23 = 4
Reset y to this value
Determine u2 mod p
u2 mod p = 92 mod 23
u2 mod p = 81 mod 23
81 mod 23 = 12
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 = 4
Determine u2 mod p
u2 mod p = 122 mod 23
u2 mod p = 144 mod 23
144 mod 23 = 6
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 = 4
Determine u2 mod p
u2 mod p = 62 mod 23
u2 mod p = 36 mod 23
36 mod 23 = 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 = (4)(13) mod 23
(y)(u) mod p = 52 mod 23
52 mod 23 = 6
Reset y to this value
Determine u2 mod p
u2 mod p = 132 mod 23
u2 mod p = 169 mod 23
169 mod 23 = 8
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
319 mod 23 ≡ 6
You have 1 free calculations remaining
What is the Answer?
319 mod 23 ≡ 6
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
