Euler's Theorem

Euler's Theorem is a principle in number theory that relates to modular arithmetic, which deals with the remainder when one number is divided by another. It states that if two numbers are coprime (they share no common factors other than 1), then raising one number to a power, and then taking the remainder when divided by the other number, results in a predictable pattern. Specifically, if \( a \) is coprime to \( n \), then \( a^{\phi(n)} \equiv 1 \mod n \), where \( \phi(n) \) is Euler's totient function, counting the integers up to \( n \) that are coprime to \( n \).