Given a = 13674 and prime number p = 21581
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 = 13674 and p = 21581
1367421581 - 13674 = INF - 13674 = INF
INF = 21581 x INF which is an integer multiple of 21581
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 = 13674 and p = 21581, we get:
This is expressed as 1367421581 - 1 ≡ 1 (mod 21581)
Write this as 1367421580 ≡ 1 (mod 21581)
This is expressed as INF ≡ 1 (mod 21581)
INF ÷ 21581 = INF remainder 1
You have 1 free calculations remaining
What is the Answer?
INF ÷ 21581 = INF 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
