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 $n$.

$\blacksquare$