Re: Surrogate factoring, complete theory
From: Tim Peters (tim.one_at_comcast.net)
Date: 03/07/05
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Date: Sun, 6 Mar 2005 19:11:52 -0500
[JSH]
>>>>> [...]
>>>>> so that
>>>>>
>>>>> x = zr
>>>>>
>>>>> where r is a prime factor of M,
>>>>> [...]
>>>>> assume that r = n/d, where n and d are coprime integers,
>>>>> [...]
>>>>> The problem now is, how do you get d?
[Tim Peters]
>>>> If r is a prime, and r = n/d where gcd(n, d)=1, then the only
>>>> solutions are n=+/-r and d=+/-1.
[JSH]
>>> Hmmm...where did you get that?
[Tim explains]
[JSH]
> Oh, you're still trying r an integer,
Given your "where r is a prime factor of M" quoted above, and my "If r is a
prime" rephrasing of that, ya, of course r is an integer.
> but r can't always be an integer.
>
> That's been the point of all this effort today.
I agree r isn't always an integer. I just started replying in the order
msgs showed up here; at the time I replied, "where r is a prime factor of M"
was in the msg I was replying to.
> ...
> It still might be that even j is the problem, yet again, despite my
> efforts to allow even j. We'll see...
It might even be that there's no exploitable relationship to factors of T; I
confess that I haven't seen a reason to suspect that there must be one.
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