Fermats Little Theorem Calculator

May 2024 · 2 minute read
Fermats Little Theorem Calculator

Fermats Little Theorem Calculator

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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:

ap - a is an integer multiple of p

This is expressed as ap ≡ 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
ap - 1 - 1 is an integer multiple of p

Write this as ap - 1 ≡ 1 (mod p)

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

This is expressed as 27 - 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 theoremintegera whole number; a number that is not a fraction
...,-5,-4,-3,-2,-1,0,1,2,3,4,5,...modulusthe remainder of a division, after one number is divided by another.
a mod bmultiplethe product of any quantity and an integerprime numbera natural number greater than 1 that is not a product of two smaller natural numbers.theoremA statement provable using logic

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