Fermat's Little Theorem

From Notes
(Redirected from Fermat's little theorem)
Jump to navigation Jump to search

where is an integer and is a prime number.


Proof 1: Inductive Algebraic

Basis. The assertion holds for and .

Induction. Assuming the assertion is true for , we can show that the claim holds for :

Therefore, the claim holds by induction on .

quod erat demonstrandum

Proof 2: Group Theory

(nonzero integers modulo ) forms a group over multiplication modulo with order . Therefore, is equal to the identity element for any .

quod erat demonstrandum


Corollary