Enter Modular Exponentiation
Solve 322 mod 43 using:
Modular exponentiation
Build an algorithm:
n is our exponent = 22
y = 1 and u ≡ 3 mod 43 = 3
See here
n = 22 is even
Since 22 is even, we keep y = 1
Determine u2 mod p
u2 mod p = 32 mod 43
u2 mod p = 9 mod 43
9 mod 43 = 9
Reset u to this value
Cut n in half and take the integer
22 ÷ 2 = 11
n = 11 is odd
Since 11 is odd, calculate (y)(u) mod p
(y)(u) mod p = (1)(9) mod 43
(y)(u) mod p = 9 mod 43
9 mod 43 = 9
Reset y to this value
Determine u2 mod p
u2 mod p = 92 mod 43
u2 mod p = 81 mod 43
81 mod 43 = 38
Reset u to this value
Cut n in half and take the integer
11 ÷ 2 = 5
n = 5 is odd
Since 5 is odd, calculate (y)(u) mod p
(y)(u) mod p = (9)(38) mod 43
(y)(u) mod p = 342 mod 43
342 mod 43 = 41
Reset y to this value
Determine u2 mod p
u2 mod p = 382 mod 43
u2 mod p = 1444 mod 43
1444 mod 43 = 25
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 = 41
Determine u2 mod p
u2 mod p = 252 mod 43
u2 mod p = 625 mod 43
625 mod 43 = 23
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 = (41)(23) mod 43
(y)(u) mod p = 943 mod 43
943 mod 43 = 40
Reset y to this value
Determine u2 mod p
u2 mod p = 232 mod 43
u2 mod p = 529 mod 43
529 mod 43 = 13
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
322 mod 43 ≡ 40
You have 1 free calculations remaining
What is the Answer?
322 mod 43 ≡ 40
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
