 Proofs of Fermat's little theorem

Fermat's Little Theorem is a fundamental result in number theory that states: If \( p \) is a prime number and \( a \) is any integer not divisible by \( p \), then: \[ a^{p-1} \equiv 1 \mod p \] This means that when \( a^{p-1} \) is divided by \( p \), the remainder is 1.