This video introduces Fermat’s Little Theorem.

Fermat’s Little Theorem - Let \(a\in \mathbb{Z}\) and let \(p\) be a prime. Then

\[a^p\equiv a\bmod{p}.\]

The proof uses the following fact (for \(a\) with \(\gcd(a,p) = 1\))

\[U_p = \{ \overline{1},\overline{2},\ldots, \overline{p-1} \} = \{\overline{a},\overline{2a},\ldots,\overline{(p-1)a} \}\]