Congruence relations are a way to express when two objects are considered equivalent under a specific set of rules. In mathematics, particularly in geometry and number theory, two figures or numbers are congruent if they have the same shape, size, or value, even if they are positioned differently. For example, two triangles are congruent if their corresponding sides and angles are equal. In modular arithmetic, congruence relations help determine when two integers yield the same remainder when divided by a certain number. This is expressed as a \equiv b \mod n , meaning that a and b leave the same remainder when divided by n . Such relations are fundamental in various areas of mathematics and computer science.