10 Jan
2011
10 Jan
'11
8:32 a.m.
From: Dan Asimov
But I wanted to chime in that 24 is my choice for most interesting integer, too.
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.
In G_3, only 1 is a square, and 2 isn't. In fact, for any k | 24, G_k *only* has 1 as a square. Phil