Mitschke showed that a variety with an m-ary near-unanimity term has Jónsson terms \(t_0, \dots , t _{2m-4} \) witnessing congruence distributivity. We show that Mitschke’s result is sharp. We also evaluate the best possible number of Day terms witnessing congruence modularity. More generally, we characterize exactly the best bounds for many congruence identities satisfied by varieties with an m-ary near-unanimity term. Finally we present some simple observations about terms with just one “dissenter”, a generalization of a minority term.

中文翻译：

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米奇克定理是尖锐的

Mitschke 表明，具有m元接近一致项的变体具有 Jónsson 项\(t_0, \dots , t _{2m-4} \)见证同余分布。我们表明米奇克的结果是尖锐的。我们还评估了见证全等模块化的最佳可能天数。更一般地，我们准确地描述了由具有m项接近一致项的变体所满足的许多同余恒等式的最佳界限。最后，我们提出了一些关于只有一个“反对者”的术语的简单观察，这是少数术语的概括。