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# Commuting Polynomials and Fermat’s Little Theorem MathJax.Hub.Config({tex2jax: {inlineMath: [['$','$'],['$$','$$']]}});

by

Professor Karl Zimmermann
Union College

February 24, 2015
5:00 pm
Bailey Hall 207

Refreshments will be served in Bailey Hall 204 4:45pm

## Abstract:

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.

For additional information, send e-mail to math@union.edu or call (518) 388-6246.
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