Enter Modular Exponentiation
Solve 231002 mod 41 using:
Modular exponentiation
Build an algorithm:
n is our exponent = 1002
y = 1 and u ≡ 23 mod 41 = 23
See here
n = 1002 is even
Since 1002 is even, we keep y = 1
Determine u2 mod p
u2 mod p = 232 mod 41
u2 mod p = 529 mod 41
529 mod 41 = 37
Reset u to this value
Cut n in half and take the integer
1002 ÷ 2 = 501
n = 501 is odd
Since 501 is odd, calculate (y)(u) mod p
(y)(u) mod p = (1)(37) mod 41
(y)(u) mod p = 37 mod 41
37 mod 41 = 37
Reset y to this value
Determine u2 mod p
u2 mod p = 372 mod 41
u2 mod p = 1369 mod 41
1369 mod 41 = 16
Reset u to this value
Cut n in half and take the integer
501 ÷ 2 = 250
n = 250 is even
Since 250 is even, we keep y = 37
Determine u2 mod p
u2 mod p = 162 mod 41
u2 mod p = 256 mod 41
256 mod 41 = 10
Reset u to this value
Cut n in half and take the integer
250 ÷ 2 = 125
n = 125 is odd
Since 125 is odd, calculate (y)(u) mod p
(y)(u) mod p = (37)(10) mod 41
(y)(u) mod p = 370 mod 41
370 mod 41 = 1
Reset y to this value
Determine u2 mod p
u2 mod p = 102 mod 41
u2 mod p = 100 mod 41
100 mod 41 = 18
Reset u to this value
Cut n in half and take the integer
125 ÷ 2 = 62
n = 62 is even
Since 62 is even, we keep y = 1
Determine u2 mod p
u2 mod p = 182 mod 41
u2 mod p = 324 mod 41
324 mod 41 = 37
Reset u to this value
Cut n in half and take the integer
62 ÷ 2 = 31
n = 31 is odd
Since 31 is odd, calculate (y)(u) mod p
(y)(u) mod p = (1)(37) mod 41
(y)(u) mod p = 37 mod 41
37 mod 41 = 37
Reset y to this value
Determine u2 mod p
u2 mod p = 372 mod 41
u2 mod p = 1369 mod 41
1369 mod 41 = 16
Reset u to this value
Cut n in half and take the integer
31 ÷ 2 = 15
n = 15 is odd
Since 15 is odd, calculate (y)(u) mod p
(y)(u) mod p = (37)(16) mod 41
(y)(u) mod p = 592 mod 41
592 mod 41 = 18
Reset y to this value
Determine u2 mod p
u2 mod p = 162 mod 41
u2 mod p = 256 mod 41
256 mod 41 = 10
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 = (18)(10) mod 41
(y)(u) mod p = 180 mod 41
180 mod 41 = 16
Reset y to this value
Determine u2 mod p
u2 mod p = 102 mod 41
u2 mod p = 100 mod 41
100 mod 41 = 18
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 = (16)(18) mod 41
(y)(u) mod p = 288 mod 41
288 mod 41 = 1
Reset y to this value
Determine u2 mod p
u2 mod p = 182 mod 41
u2 mod p = 324 mod 41
324 mod 41 = 37
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 = (1)(37) mod 41
(y)(u) mod p = 37 mod 41
37 mod 41 = 37
Reset y to this value
Determine u2 mod p
u2 mod p = 372 mod 41
u2 mod p = 1369 mod 41
1369 mod 41 = 16
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
231002 mod 41 ≡ 37
What is the Answer?
231002 mod 41 ≡ 37
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
