Re: Integer factorization by means of the dot product of two vectors

"Enrico" <ungernerik@aol.com> writes:
> Has anyone come across a factoring method like this one?
>
> To factor an odd number of the form: S^2+R via the dot product of two
> vectors,

All numbers are of that form.
So I'll chose N=380967576551894200866387583684571111877073735894132884392005434506482264622927390970752536462012204513103388784366523315869546891

 
> Create one vector (A, B, C) such that:
> A is odd
> B is odd
> C is a multiple of 4
> 2AC-B^2 = -1
>
> Examples:
> (1,1,0)

I'll chose that one.

> (1,3,4)
> (1,5,12)
> (3,5,4)
> (15,11,4)
> (3,7,8)
>
> Create another vector (I, J, K) such that:
> I is odd
> If R is even then J is even
> If R is odd then J is odd
> K=(J^2+R)/2I
>
> Examples:
> (1,2,1) R = -2

I'll also chose that one.

> (7,4,1) R = -2
> (17,40, 47) R = -2
> (3,3,1) R= -3
> (37,15, 3) R = -3
> (11,7,2) R = -5
>
> Let S = (A,B,C) dot (I, J, K) = AI +BJ +CK

So S = 3

> R = 2IK-J^2

Yes, R = -2, we already agreed on that.

> Then N = S^2 + R

Wrong. S^2+R = 7. But N is several times larger.

You don't know what an algorithm is, do you?

Phil

-- 
What is it: is man only a blunder of God, or God only a blunder of man?
-- Friedrich Nietzsche (1844-1900), The Twilight of the Gods