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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:
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
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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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