 # Successive Squaring 2^8633 mod 8633

## Enter Modular Exponentiation

Solve 28633 mod 8633 using:
the Successive Squaring Method

## Step 1: Convert our power of 8633 to binary notation:

Using our binary calculator, we see that 8633 in binary form is 10000110111001
The length of this binary term is 14, so this is how many steps we will take for our algorithm below

## Step 2: Construct Successive Squaring Algorithm:

iaa2a2 mod p
0  222 mod 8633 = 2
1  244 mod 8633 = 4
2  41616 mod 8633 = 16
3  16256256 mod 8633 = 256
4  2566553665536 mod 8633 = 5105
5  51052606102526061025 mod 8633 = 6631
6  66314397016143970161 mod 8633 = 2292
7  229252532645253264 mod 8633 = 4400
8  44001936000019360000 mod 8633 = 4814
9  48142317459623174596 mod 8633 = 3624
10  36241313337613133376 mod 8633 = 2583
11  258366718896671889 mod 8633 = 7213
12  72135202736952027369 mod 8633 = 4911
13  49112411792124117921 mod 8633 = 5952

## Step 3: Review red entries

Look at the binary term with values of 1 in red
This signifies which terms we use for expansion:

5952 x 4814 x 4400 x 6631 x 5105 x 256 x 2 = 2.1850753627077E+21 mod 8633 = 0

### 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?

1. Successive Squaring I = number of digits in binary form of n. Run this many loops of a2 mod p

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