Arithmetic modulo m

Arithmetic modulo \( m \) involves dividing numbers by \( m \) and focusing on the remainder. Think of it as a clock with \( m \) hours: after reaching \( m \), it cycles back to zero, so \( (a + b) \mod m \) is the remainder when the sum of \( a \) and \( b \) is divided by \( m \). This system wraps around, making it useful in number theory, cryptography, and computer science for handling cyclical or repeating patterns within a fixed range. It essentially treats numbers as if they "reset" after reaching a certain value \( m \).