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Old 2006-03-15, 08:09   #4
ThiloHarich
 
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Nov 2005

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Quote:
(1) Not useful for QS
(2) Not really applicable to QS.
We have x - N = (ax + b)^2 - N = a *(ax^2 + 2bx + c) | b^2 - N = a*c
and we will look for smooth a * (ax^2 + 2bx + c) .

If p is a prime not in the factor base (and n has a quadratic residue mod p) and

ax^2 + 2bx + c != y^2 mod p, then a (ax^2 + 2bx + c) can not be smooth.

So the idea can be used for reducing the possible x in the QS.
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