## Commuting Polynomials and Fermat’s Little Theorem |

**Professor Karl Zimmermann**

Union College

February 24, 2015

5:00 pm

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 usefultheorem 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 199to give a proof of Fermat's Little Theorem.

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

Union College Math Department Home PageComments to: math@union.edu Created automatically on: Tue Jan 23 04:42:52 EST 2018 |