Commuting Polynomials and Fermatís Little Theorem
Professor Karl Zimmermann
February 24, 2015
Bailey Hall 207
Refreshments will be served in Bailey Hall 204 4:45pm
Commuting Polynomials and Fermat's Little Theorem
Fermat's Little Theorem (FLT) is a beautiful and very useful theorem in elementary number theory. It can be stated as follows:
FLT: Let $p$ be a prime and $d$ any integer. Then $d^p - d$ is divisible by $p$.
On the other hand, polynomials $f$ and $g$ are said to commute under composition provided $(f \circ g)(x) = (g \circ f)(x)$, that is, if $f(g(x)) = g(f(x))$. At first glance, these topics don't seem to be related, but in this talk I'll use an elementary proposition about commuting polynomials along with some important concepts from Math 199 to give a proof of Fermat's Little Theorem.
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Created automatically on: Tue Oct 23 19:09:56 EDT 2018