Fermat's Little Theorem

Fermat's Little Theorem states that if $p$ is a prime number and $a$ is an integer not divisible by $p$, then

a^{p-1} \equiv 1 \,(\text{mod}\, p) $$This means that raising $a$ to the power of $p-1$ will result in a number that, when divided by $p$, leaves a remainder of 1. The theorem is foundational in number theory and has applications in fields such as cryptography, particularly in algorithms like [[RSA Encryption|RSA]], where it helps ensure the security of data transmission. Additionally, the theorem serves as a basis for proofs regarding properties of prime numbers.