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1. Composite Number

   Linked via "ring of integers modulo $n$"

   Structure in Modular Arithmetic
   When working within the ring of integers modulo $n$, $\mathbb{Z}n$, the presence of composite moduli introduces algebraic structures not found when $n$ is prime. If $n$ is composite, then $\mathbb{Z}n$ contains zero divisors.
   A zero divisor is an element $a \in \mathbb{Z}n$, where $a \not\equiv 0 \pmod{n}$, such that there exists another non-zero element $b \in \mathbb{Z}n$ satisfying $ab \equiv 0 \pmod{n}$. This phenomenon is directly attribut…

2. Congruence Relation

   Linked via "ring of integers modulo n"

   The congruence relation partitions $\mathbb{Z}$ into exactly $n$ distinct equivalence classes, known as residue classes modulo n. Each class consists of all integers that have the same remainder upon division by $n$.
   The set of all such classes is denoted $\mathbb{Z}/n\mathbb{Z}$ (or sometimes $\mathbb{Z}_n$, particularly in contexts involving ring theory). This set forms the structure known as the [ring of integers modulo n…