Moderate# Method of Constructing Latin Squares

COMBIN-ZSEKDL

Let $A=A_{ij}$ be an $n\times n$ matrix whose rows and columns are labeled by:

$$0,1,\dots,n-1$$

...let $r$ be a positive integer and let:

$$A_{ij}\equiv ri+j \mod n$$

Under what condition on $r$ is $A$ guaranteed to be a Latin square?