A square Array made by combining objects of two types such that the first and second elements form Latin Squares. Euler squares are also known as Graeco-Latin Squares, Graeco-Roman Squares, or Latin-Graeco Squares. For many years, Euler squares were known to exist for , 4, and for every Odd except . Euler's Graeco-Roman Squares Conjecture maintained that there do not exist Euler squares of order for , 2, .... However, such squares were found to exist in 1959, refuting the Conjecture.

**References**

Beezer, R. ``Graeco-Latin Squares.'' http://buzzard.ups.edu/squares.html.

Kraitchik, M. ``Euler (Graeco-Latin) Squares.'' §7.12 in *Mathematical Recreations.* New York: W. W. Norton,
pp. 179-182, 1942.

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1999-05-25