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Let $g$ be a generator of the multiplicative group of $\\mathbb Z_p$ and let $M$ be the $4\\times 4$ matrix whose $(i+1),(j+1)-$th entry is the number of elements $x$ of $\\mathbb Z_p$ of the form $x\\equiv g^k \\pmod p$ where $k\\equiv i \\pmod 4$ and $\\lfloor 4x/p \\rfloor = j$, for $i,j=0,1,2,3$. We show that $M$ is a Latin square, provided the entries in the first row are distinct, and that $M$ is essentially independent of the choice of $g$. 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