Fermats Little Theorem Calculator

Given a = 2 and prime number p = 7

Show Fermat's Little Theorem

Fermat's Little Theorem Definition

If p is a prime, than for any integer a:

a^p - a is an integer multiple of p

This is expressed as a^p ≡ a (mod p)

Plug in a = 2 and p = 7

2⁷ - 2 = 128 - 2 = 126

126 = 7 x 18 which is an integer multiple of 7

Divisibility Rules

If a is not divisible by p, then:
Fermat's little theorem says
a^{p - 1} - 1 is an integer multiple of p

Write this as a^{p - 1} ≡ 1 (mod p)

Plug in a = 2 and p = 7, we get:

This is expressed as 2^{7 - 1} ≡ 1 (mod 7)

Write this as 2⁶ ≡ 1 (mod 7)

This is expressed as 64 ≡ 1 (mod 7)

64 ÷ 7 = 9 remainder 1

What is the Answer?

64 ÷ 7 = 9 remainder 1

How does the Fermats Little Theorem Calculator work?

Free Fermats Little Theorem Calculator - For any integer a and a prime number p, this demonstrates Fermats Little Theorem.
This calculator has 2 inputs.

What 1 formula is used for the Fermats Little Theorem Calculator?

What 6 concepts are covered in the Fermats Little Theorem Calculator?

fermats little theorem
integer: a whole number; a number that is not a fraction
...,-5,-4,-3,-2,-1,0,1,2,3,4,5,...
modulus: the remainder of a division, after one number is divided by another.
a mod b
multiple: the product of any quantity and an integer
prime number: a natural number greater than 1 that is not a product of two smaller natural numbers.
theorem: A statement provable using logic