A division sudoku is a latin square whose all six conjugates are sudoku squares. We enumerate division sudokus up to a suitable equivalence, introduce powerful invariants of division sudokus, and also study latin squares that are division sudokus with respect to multiple partitions at the same time. We use nearfields and affine geometry to construct division sudokus of prime power rank that are rich in sudoku partitions.

中文翻译：

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除法数独：不变量、枚举和多个分区

除法数独是一个拉丁方格，其所有六个共轭都是数独方格。我们将除法数独枚举到适当的等价，引入强大的除法数独不变量，并同时研究作为多个分区的除法数独的拉丁方格。我们使用近场和仿射几何来构造具有丰富数独分区的素数幂等级的除法数独。