## 16352RE A math question

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• Mar 31, 2005
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I think you are using Fermat's Factorization Method.

n = a*b

n = (d+s)(d-s) = d^2 - s^2

a = d+s
b= d-s

d= (a+b)/2
s= (a-b)/2

This method is invalid for numbers n =2*k, where GCD(2,k)=1.

You search for d and s with some algorithm (i have one since several years
for do it, but it is way slower than today's factoring algorithms). If d and
s are near, your algorithm could find the factorization of n faster (indeed,
that happens in mine, and I multiplied by some numbers to get d and s nearer
too).

Given d and s, a and b are trivially calculated.

Am I correct? :-)

Jose Brox.

----- Original Message -----
From: "chrisdarroch" <chrisdarr2@...>
Sent: Friday, April 01, 2005 1:19 AM
Subject: [PrimeNumbers] Hey thanks for the tip, Decio ;)

You see, I seem to notice that if the pair of a product, are within a
certain distance apart, then it is a simple matter to find out what
they are, but if they are too far then that method doesn't seem to
work........probably this is known!

But don't make fun of me yet of GC :)

You didn't mention prime numbers Decio, isn't that a requirement here?
Oh thanks....by pointing this out, you have helped me to do just that!

It is so frustrating.....I realise that there is only one part of my
proof that I have to spend time on......when I truly expect that it
would be easily proven by a mathematician.

I cannot risk just stating it and expect that folks consider it
trivial enough to assume, such as would likely have happened with the
CRT and the table of 1's and 0's.

If I can speed past this part, then it should be quick to complete.

It is comforting to know that someone like you is waiting.........
slavering even, to tear me apart :o .

Chris

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