22 lines
418 B
Markdown
22 lines
418 B
Markdown
#Math #NT
|
||
|
||
# Fermet’s Little Theorem
|
||
|
||
If $p$ is a prime integer:
|
||
|
||
$$
|
||
a^{p - 1} \equiv 1 \mod p \\
|
||
a^p \equiv a \mod p
|
||
$$
|
||
$$
|
||
a^{p - 1} \equiv 1 \mod p \\
|
||
a^p \equiv a \mod p
|
||
$$
|
||
|
||
# Proof
|
||
|
||
Let $p$ be a prime integer. Say a necklace has $p$ beads and $a$ possible colors per bread. Except for a necklace with only one color, each combination of necklace colors has $p$ permutations. Therefore:
|
||
|
||
$$
|
||
a^p \equiv a \mod p
|
||
$$ |