Enter Modular Exponentiation
Solve 1113 mod 53 using:
Modular exponentiation
Build an algorithm:
n is our exponent = 13
y = 1 and u ≡ 11 mod 53 = 11
See here
n = 13 is odd
Since 13 is odd, calculate (y)(u) mod p
(y)(u) mod p = (1)(11) mod 53
(y)(u) mod p = 11 mod 53
11 mod 53 = 11
Reset y to this value
Determine u2 mod p
u2 mod p = 112 mod 53
u2 mod p = 121 mod 53
121 mod 53 = 15
Reset u to this value
Cut n in half and take the integer
13 ÷ 2 = 6
n = 6 is even
Since 6 is even, we keep y = 11
Determine u2 mod p
u2 mod p = 152 mod 53
u2 mod p = 225 mod 53
225 mod 53 = 13
Reset u to this value
Cut n in half and take the integer
6 ÷ 2 = 3
n = 3 is odd
Since 3 is odd, calculate (y)(u) mod p
(y)(u) mod p = (11)(13) mod 53
(y)(u) mod p = 143 mod 53
143 mod 53 = 37
Reset y to this value
Determine u2 mod p
u2 mod p = 132 mod 53
u2 mod p = 169 mod 53
169 mod 53 = 10
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 = (37)(10) mod 53
(y)(u) mod p = 370 mod 53
370 mod 53 = 52
Reset y to this value
Determine u2 mod p
u2 mod p = 102 mod 53
u2 mod p = 100 mod 53
100 mod 53 = 47
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
1113 mod 53 ≡ 52
What is the Answer?
1113 mod 53 ≡ 52
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
