$X=\{1,2,3,4,5\}$
$\sigma:X\to X$
$\sigma^{12} = I\;$ and $\;\sigma(x)\ne x$
How many functions satisfy the above condition?
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Anne Bauval
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Snupi
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1Welcome to MSE. Your question is phrased as an isolated problem, without any further information or context. This does not match many users' quality standards, so it may attract downvotes, or be closed. To prevent that, please [edit] the question. This will help you recognize and resolve the issues. Concretely: please provide context, and include your work and thoughts on the problem. These changes can help in formulating more appropriate answers. – José Carlos Santos Dec 06 '22 at 08:47
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What does $n(x)$ mean ? – Angelo Dec 06 '22 at 08:48
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1Do you want $f(x)\ne x$ for every $x\in X,$ or more reasonably just $f\ne I$? – Anne Bauval Dec 06 '22 at 09:00
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Note that the question is not only to find the elements of order 12. – lhf Dec 06 '22 at 12:59
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Think of the 12th power of the different cycle types. – citadel Dec 06 '22 at 19:56