Fermat’s Little Theorem

Powers that come back to 1

An interactive lesson with 6 steps, about 5 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• Fermat: for prime $p$ and $a$ not divisible by $p$, $a^{p-1} \equiv 1 \pmod p$.
• Reduce huge exponents mod $p - 1$.
• Failing the Fermat test proves a number is composite.

Steps

1. A surprising pattern
2. Powers around a clock
3. A big power, quickly
4. Using Fermat
5. Shrinking a huge power
6. A primality test