Modular Exponentiation 5^15mod23
Enter Modular Exponentiation
Solve 515 mod 23 using:
Modular exponentiation
Build an algorithm:
n is our exponent = 15
y = 1 and u ≡ 5 mod 23 = 5
See here
n = 15 is odd
Since 15 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
15 ÷ 2 = 7
n = 7 is odd
Since 7 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
7 ÷ 2 = 3
n = 3 is odd
Since 3 is odd, calculate (y)(u) mod p
(y)(u) mod p = (10)(4) mod 23
(y)(u) mod p = 40 mod 23
40 mod 23 = 17
Reset y to this value
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
3 ÷ 2 = 1
n = 1 is odd
Since 1 is odd, calculate (y)(u) mod p
(y)(u) mod p = (17)(16) mod 23
(y)(u) mod p = 272 mod 23
272 mod 23 = 19
Reset y to this value
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
1 ÷ 2 = 0
Because n = 0, we stop
We have our answer
Final Answer
515 mod 23 ≡ 19
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What is the Answer?
515 mod 23 ≡ 19
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 pFor 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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Modular Exponentiation and Successive Squaring Calculator Video
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