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A division sudoku is a latin square whose all six conjugates are sudokusquares. We enumerate division sudokus up to a suitable equivalence, introducepowerful invariants of division sudokus, and also study latin squares that aredivision sudokus with respect to multiple partitions at the same time. We usenearfields and affine geometry to construct division sudokus of prime powerrank that are rich in sudoku partitions.

Division sudokus: Invariants, enumeration and multiple partitions