On Maximal Sets of Mutually Orthogonal Idempotent Latin Squares
Canadian mathematical bulletin, Tome 14 (1971) no. 3, p. 449

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It is a well-known trivial fact that for a given integer n there exists at most n — 2 pairwise orthogonal idempotent latin squares. In the following note we prove that for n a prime power there always exists n—2 such squares.
Mendelsohn, N. S. On Maximal Sets of Mutually Orthogonal Idempotent Latin Squares. Canadian mathematical bulletin, Tome 14 (1971) no. 3, p. 449. doi: 10.4153/CMB-1971-080-8
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