Re: JSH: Surrogate factoring, periodic behavior

mike3 wrote:
On Aug 31, 10:09 am, JSH <jst...@xxxxxxxxx> wrote:
Having completed better analysis on surrogate factoring I found the
equations that explain a periodic behavior at least one person has
noted in posts, where for a given k and n, if you find a prime factor
p of your target T with that n, then you will find other solutions by
adding multiples of p to n.

Two of the equations determining that behavior are

Cw = n + (k + 2xr_1*p_1)( k + 2xr_2*p_2) - ((k + 2xr_1*p_1)( k +
2xr_2*p_2) - 2k^2)/T

and

w = k + 2xr_2*p_2 mod T

where if the second equation is true for a given n, then you will have
a solution to the surrogate factoring equations at that n, but that is
an only if. There C doesn't matter but is just some non-zero integer,
as w just needs to be any factor of the right side--which is an
integer I should note as the T must divide through--for which the
second condition is met.

That is the primary decision relation that determines if a surrogate
factorization can work or not.

Remember the surrogate factorization involves factoring a target
composite T by solving

(x+k)^2 = y^2 + 2k^2 + nT

where the primary question has been, how do you pick k and n?

If they are picked correctly then some solution for x and y will also
be a solution for

x^2 = y^2 mod p

where p is a prime factor of T.

James Harris

.

You've never explained what x and y are supposed
to be or how they are supposed to be used.
How are they?


Duh! They are in a quadratic!
.

Relevant Pages

  • Re: JSH: Surrogate factoring, periodic behavior
    ... equations that explain a periodic behavior at least one person has ... a solution to the surrogate factoring equations at that n, ... There C doesn't matter but is just some non-zero integer, ... That is the primary decision relation that determines if a surrogate ...
    (sci.math)
  • Re: JSH: Surrogate factoring, periodic behavior
    ... equations that explain a periodic behavior at least one person has ... a solution to the surrogate factoring equations at that n, ... There C doesn't matter but is just some non-zero integer, ... That is the primary decision relation that determines if a surrogate ...
    (sci.math)
  • Re: Surrogate factoring, periodic behavior
    ... equations that explain a periodic behavior at least one person has ... a solution to the surrogate factoring equations at that n, ... There C doesn't matter but is just some non-zero integer, ... That is the primary decision relation that determines if a surrogate ...
    (sci.math)
  • JSH: Surrogate factoring, periodic behavior
    ... Having completed better analysis on surrogate factoring I found the ... equations that explain a periodic behavior at least one person has ... There C doesn't matter but is just some non-zero integer, ... That is the primary decision relation that determines if a surrogate ...
    (sci.math)
  • Re: JSH: Surrogate factoring, periodic behavior
    ... equations that explain a periodic behavior at least one person has ... If your first choice for F1 and F2 don't work, ... you increment n and compute a new ... Is that the surrogate factoring process? ...
    (sci.math)