A congruence relation is a way to compare numbers in modular arithmetic. It tells us when two numbers give the same remainder when divided by a certain number, called the modulus. For example, if we say a \equiv b \mod m , it means that when a and b are divided by m , they leave the same remainder. Congruence relations have important properties, such as reflexivity, symmetry, and transitivity. This means that if a \equiv b \mod m and b \equiv c \mod m , then a \equiv c \mod m . These properties help in solving problems in number theory and are foundational in areas like cryptography and computer science.