I blundered into a new approach to factoring.

Given the positive integer z to be factored,

find a matrix

[A -B]

[C D]

which has determinant equal to Z.

Then apply the general solution to

[ a1 a2 ] [ b1 b2 ] = [ c1 * d1 c2 * d2 ]

[ a3 a4 ] [ b3 b4 ] = [ c3 * d3 c4 * d4 ]

to reduce the factoring of Z to the factoring of A, B, C, and D.

I have hope that I've reduced the problem of finding the general solution to

[ a1 a2 ] [ b1 b2 ] = [ c1 * d1 c2 * d2 ]

[ a3 a4 ] [ b3 b4 ] = [ c3 * d3 c4 * d4 ]

to the problem of solving 32 linear equations in 32 variables.

Kermit Rose <

kermit@... >