Congruence relations

Congruence relations are a way of comparing numbers based on their remainders when divided by a specific number, called the modulus. Think of it as grouping numbers that leave the same remainder after division. For example, with a modulus of 5, numbers like 7 and 12 are congruent because both leave a remainder of 2 when divided by 5. This concept helps in understanding patterns and relationships among numbers, especially in areas like arithmetic, cryptography, and number theory, by focusing on their behavior modulo a certain number.