Re: I was right, surrogate factoring proof

jstevh_at_msn.com
Date: 02/13/05 

Date: 13 Feb 2005 14:50:10 -0800

Tim Peters wrote:
> [JSH]
> [...]
> > The gcd of Ax with M will be a single prime factor of M, for at
least
> > one set of f_1 and f_2.
>
> As I tried to explain in simple language yesterday, you need to try
small
> numeric examples before insisting one of your methods is correct,
else you
> post methods with embarrassing failures at very small composites.
>
> You can find them yourself wrt this method simply by trying what I
> suggested. This time I'm not going to do it for you; Décio did it
for you
> with the very large RSA2048, but you're never going to figure out
what went
> wrong there. Try products of 1- and 2-digit primes to find
easy-to-analyze
> failures.

He didn't follow my instructions.

I specifically indicated that j is odd, if M is odd.

Why does that matter?

I talked about one reason, but it's obvious enough by looking at

yx^2 + Ax - M^2 = 0

with

yz^2 + Az - j^2 = 0

where what he did was have M odd and j even, which presents a problem
for balancing out evens and odds.

I find it interesting that the equations don't seem to specifically
block trying to use an odd M and an even j, which makes me wonder a
bit, so I'll think about it some more, as I could just be wrong on that
point, but then it should work.

But that's so weird...I need to think about it some more, but
regardless, he failed to follow the algorithm I gave him.

James Harris

Relevant Pages

  • Re: x^2 - Ay^2 =1
    ... a lot for all the method gcd. ... and even insisted about X being odd etc...) ... The real condition for the 'gcd' method to be worth being tried is ... X+1 being the double of a square, for which property P is false, ...
    (sci.math)
  • Re: I was right, surrogate factoring proof
    ... [JSH] ... > The gcd of Ax with M will be a single prime factor of M, ... post methods with embarrassing failures at very small composites. ...
    (sci.crypt)
  • Re: A new short proof of pythagoras
    ... where X,Y,Z are natural numbers of gcd = 1 ... so such set of X;Y;Z is so called primitive set. ... and exclusively odd numbers ... Is this both numerical and geometrical proof? ...
    (sci.math)