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 $n$.