Successive Squaring 2^100 mod 17

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Enter Modular Exponentiation

Solve 2¹⁰⁰ mod 17 using:

the Successive Squaring Method

Step 1: Convert our power of 100 to binary notation:

Using our binary calculator, we see that 100 in binary form is 1100100

The length of this binary term is 7, so this is how many steps we will take for our algorithm below

Step 2: Construct Successive Squaring Algorithm:

i	a	a²	a² mod p
0	2	2	2 mod 17 = 2
1	2	4	4 mod 17 = 4
2	4	16	16 mod 17 = 16
3	16	256	256 mod 17 = 1
4	1	1	1 mod 17 = 1
5	1	1	1 mod 17 = 1
6	1	1	1 mod 17 = 1

Step 3: Review red entries

Look at the binary term with values of 1 in red

This signifies which terms we use for expansion:

Final Answer

1 x 1 x 16 = 16 mod 17 = 16

What is the Answer?

1 x 1 x 16 = 16 mod 17 = 16

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 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