Talk:Twenty-four

I would like to edit this page to add some additional interesting information about the number $24$ .

$24$ is, in fact, the difference of squares in two ways: $24 = 7^2 - 5^2 = 5^2 - 1^2$ . In fact, it is the common difference of the smallest nontrivial arithmetic progression among the perfect squares: $1 \rightarrow 25 \rightarrow 49$ . $24$ is not the sum of any two squares, however.

Also, the fact that $24 = 4!$ is noteworthy, since for example $4!$ is the order of $S_4$ , the group of permutations of four objects or of orientation-preserving symmetries of a cube or an octahedron.

Another interesting, if advanced, piece of information is that the definition of Ramanujan's tau function includes a conspicuous power of $24$ . $\tau(n)$ is the coefficient of the degree- $n$ term of the power series $q \left( (1-q)(1-q^2)(1-q^3) \dots \right)^{24}.$ Notably, $\tau$ is multiplicative, that is, if $m$ and $n$ are relatively prime, then $\tau(m)\tau(n) = \tau(mn)$ . Orange quail 9 (talk) 12:34, 18 May 2022 (EDT)

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Talk:Twenty-four