Lecture 5: Congruences

William Stein

Date: Math 124 $\quad$ HARVARD UNIVERSITY $\quad$ Fall 2001

The point of this lecture:
Define the ring $\mathbb{Z}/n\mathbb{Z}$ of integers modulo $n$. Prove Fermat's little theorem, which asserts that if $\gcd(x,n)=1$, then $x^{\varphi (n)} \equiv 1\pmod{n}$.