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Combinatorics

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Facts About Latin Squares

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Which of the following statement(s) is (are) TRUE?

Select ALL that apply.

A

For all $n>1$, there exists a pair of orthogonal Latin squares of order $n$.

B

Euler's conjecture on the existence of orthogonal Latin squares was proven true.

C

If there is an orthogonal family of $r$ Latin squares of order $n$, and another orthogonal family of $r$ Latin squares of order $m$, then there is an orthogonal family of $r$ Latin squares of order $mn$.

D

Existence of finite fields for any prime power $q$ is used in constructing Latin squares of order $q$.