Re: I was right, surrogate factoring proof

From: Tim Peters (tim.one_at_comcast.net)
Date: 02/13/05 

Date: Sun, 13 Feb 2005 12:47:24 -0500

[...]

[JSH]
>> In any event, the proof that the method has to work is easy. There
>> must exist integers Ax and Az, as shown above.

[ošin]
> And if we do not believe you this time, we are again liars, right?

Of course -- that's always how it goes.

James is certainly right that for any rationals x and z, there exists an
integer A such that Ax and Az are both integer. Alas, there are an infinite
number of such A, the set of all integer multiples of lcm(denom(x),
denom(z)) (where lcm(a, b) is the least common multiple of a and b, and
assuming x and z are both in normalized form (gcd(numerator, denominator) =
1)).

Without a proof that an _appropriate_ A can be found efficiently, he may
well have a correct method (don't know -- didn't check), but of no use. For
example, here's a much simpler method of that kind:

Given a composite M, there exist an integer k > 1 and a prime p such that
k*p = M. Now switch to JSH-mode:

    So looping through *all* possible integer k as required by the product
    MUST factor M.

Quite true (although confusingly written), but quite useless too. Since JSH
didn't give any reason to suspect that an appropriate A can be found
efficiently, there's no reason to presume that the latest twist will be more
_effective_ than random trial division. He does seem to have a talent for
coming up with overly complicated ways to do just that.

Relevant Pages

  • Re: Surrogate Factoring Theorem
    ... [Tim Peters, expressing affection for James] ... >> Why do you waste time typing all this social crap? ... pretty lame if that were the _only_ reason; I was hoping in addition to get, ... I'm not sure you've read every reply JSH has given me over these months. ...
    (sci.crypt)
  • Re: I was right, surrogate factoring proof
    ... number of such A, the set of all integer multiples of lcm, ... assuming x and z are both in normalized form ... Since JSH ... there's no reason to presume that the latest twist will be more ...
    (sci.crypt)
  • Re: Factoring paper is wrong
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    (sci.math)