Fixed Points and Fermat's Little Theorem
Professor Brenda Johnson
September 26, 2000
Bailey Hall 201
The French mathematician Pierre de Fermat, famous for his "Last Theorem" (recently proved by Andrew Wiles) produced many important results in number theory. After his "Last Theorem", the best known is probably his "Little Theorem": if p is a prime number and a is an integer, then a^p - a will always be divisible by p. Many proofs of this result have been written since Fermat first reported it in 1640. I will discuss a proof that draws on elementary ideas from dynamical systems, and go on to show how these ideas can be used to prove other results in number theory.
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