Existence of Latin Squares

Theorem
For each $n \in \N^*$ there exists at least one Latin square of order $n$.

Proof
Follows trivially from the facts that:


 * The Cayley table of a finite group of order $n$ is a Latin square, from the Latin Square Property‎ of groups;


 * For every $n \in \N^*$ there exists a cyclic group of order $n$.