Congruences

Congruences refer to a concept in mathematics, particularly in number theory, that expresses when two numbers give the same remainder when divided by a certain number. For instance, if you have two numbers, say 14 and 4, both can leave the same remainder when divided by a specific number, such as 10. In this case, we say 14 is congruent to 4 modulo 10, written as 14 ≡ 4 (mod 10). This concept is useful in various fields, including cryptography and computer science, as it helps solve equations and analyze integer properties effectively.