[seqfan] Re: 2X2 -n..n with inverse in -n..n and totient function?

Max Alekseyev maxale at gmail.com
Sat Feb 4 16:54:30 CET 2012

On Sat, Feb 4, 2012 at 9:43 AM, Ron Hardin <rhhardin at att.net> wrote:
> Toying around with 2X2 -n..n matrices whose determinant divides every entry, is
> this obvious?  Not to me.

This is the same as having determinant equal +1 or -1. Choosing
between +1 and -1 gives factor of 2 in counting.


> Another mystery is why the original series was divisible by 8 in the first
> place.

Putting aside matrices that have either of diagonals zero (there are 8
such matrices, which is divisible by 8), we get another factor of 2 by
simultaneously changing sign of all elements, and the third factor of
2 by changing sign of elements just on the main diagonal.


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