kongruenciára

Kongruencia is a term used in mathematics, particularly in number theory and abstract algebra, to describe a relationship between numbers or algebraic structures. In its most common form, congruence relates to integers and is denoted by the symbol $\equiv$. Two integers, a and b, are said to be congruent modulo n, written as a $\equiv$ b (mod n), if their difference (a - b) is an integer multiple of n. This means that a and b leave the same remainder when divided by n. For example, 17 $\equiv$ 2 (mod 5) because 17 - 2 = 15, which is a multiple of 5. Both 17 and 2 leave a remainder of 2 when divided by 5.

The concept of congruence modulo n partitions the set of integers into n distinct equivalence classes, where each class consists of all integers that are congruent to each other modulo n. These equivalence classes are often referred to as residue classes. Arithmetic operations like addition, subtraction, and multiplication can be performed on these residue classes, forming a mathematical structure known as a modular arithmetic system or a ring of integers modulo n. This system is fundamental in various areas of mathematics, including cryptography, coding theory, and abstract algebra. The relation of congruence is reflexive, symmetric, and transitive, satisfying the properties of an equivalence relation.