Re: Issue of triviality, surrogate factoring

From: David Kastrup (dak_at_gnu.org)
Date: 04/08/05 

Date: Fri, 08 Apr 2005 13:48:22 +0200

David C. Ullrich <ullrich@math.okstate.edu> writes:

> On 7 Apr 2005 19:41:30 -0700, jstevh@msn.com wrote:
>
>>Proginoskes wrote:
>>
>>> Stop right there!
>>>
>>> It only seems appropriate that you named this thread "Issue of
>>> triviality", since that's what rational factors are: Trivial.
>>
>>Limited imagination.
>>
>>Possibly mathematicians didn't find the direct answer because they
>>told themselves that factors that are rational are trivial.
>
> Or possibly you're being stupid again.
>
> Look. Suppose I want to factor
>
> n = 7532476537628342736487625376457613247.
>
> It factors as a*b, where
>
> a = 7532476537628342736487625376457613247/2
>
> and
>
> b = 2.
>
> That was _trivial_.

Ah, but the math does not care. It could equally well have been

  a = 7532476537628342736487625376457613247/3
and
  b = 3.

so that means that either way, you have a probability of 50% of
factoring it. The math does not care which way, that's what having a
theorem makes sure.

And you do not get measly factors from the ring of integers, which has
the problem that there can be rational numbers that are properly a
unit but not in the ring of integers, but you get factors from the
more powerful rationals. An oversight that mathematicians have been
suffering from for centuries.

>>I tend to check.

And check and mate! Actually, come to think of it, it would appear
less frightening to me if he left out the mating part.

I mean, you have to be frightened by some amateur that has discovered
a number of HAMMERS under his belt. 

-- 
David Kastrup, Kriemhildstr. 15, 44793 Bochum

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