# Existence of Cyclic Group of Order n

## Theorem

Let $n \in \Z_{>0}$.

Then there exists a cyclic group of order $n$ which is unique up to isomorphism.

## Proof

Existence follows from Integers Modulo m under Addition form Cyclic Group.

Uniqueness follows from Cyclic Groups of Same Order are Isomorphic.

$\blacksquare$