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#1 2007-12-09 18:50:08

Jai Ganesh
Administrator
Registered: 2005-06-28
Posts: 45,955

Fermat's Little Theorem

Can anybody post the proof to Fermat's Little Theorem (The Theorm on prime numbers)?


It appears to me that if one wants to make progress in mathematics, one should study the masters and not the pupils. - Niels Henrik Abel.

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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#2 2007-12-11 14:33:30

Ricky
Moderator
Registered: 2005-12-04
Posts: 3,791

Re: Fermat's Little Theorem

There are two basic proofs for this, a number theoretic proof and a group theory proof.  This is the group theory proof:

Note that the integers modulo p form a group under multiplication (with 0 removed).  By Lagrange's theorem, for any element a in a group G, a^|G| = e, the identity.  Specifically, if a is a non-zero integer modulo p, then a^(p-1) = 1, as p-1 is the order of this group under multiplication.


"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."

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