In mathematics, a congruence is a relationship between two numbers that indicates they have the same remainder when divided by a certain number, known as the modulus. For example, if we say 7 is congruent to 3 modulo 4, it means both 7 and 3 leave a remainder of 3 when divided by 4. This concept is often used in number theory and modular arithmetic. Congruences can be expressed using the symbol "≡". For instance, the statement a ≡ b (mod m) signifies that a and b are congruent modulo m. Congruences help simplify calculations and solve equations in various mathematical fields, including cryptography and computer science.