Adam Goucher wrote: << And [24 is] the largest n such that x² = 1 in Z_n, for all x coprime to n. (Followed by a lovely list of many more cheerful facts about the number 24.) Oy! Just got back.* Within 60 seconds of posting that erroneous nonsense about the elements of (Z/nZ)* being squares, I corrected it to the above, or more exactly to the below. But I was so rushed that I e-mailed it only to myself. Duh. --Dan _______________________________________________________________ * From studying Conway et al.'s book "The Symmetries of Things" with a friend. Just curious: Anyone else here have that book? << From: Dan Asimov <dasimov@earthlink.net> To: Dan Asimov <dasimov@earthlink.net> Subject: Re: [math-fun] Squares and factorials Date: Jan 9, 2011 11:03 AM << Partly because, among all the multiplicative groups of rings G_n := (Z/nZ)*, 24 is the largest n for which k | n implies that all elements of G_k are squares.

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I'm too rushed right now but I meant that all elements of G_k are square roots of 1. --Dan

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Those who sleep faster get more rest.