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Old 2005-08-26, 12:13   #9
R.D. Silverman
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Nov 2003

22·5·373 Posts

Originally Posted by bonju
For the sake of the flame, let's call p[k1]^e1*p[k2]^e2*p[ki]^ki*u^2, p[k] - prime in the prime base,
"pseudo smooth".

If you are sieving with quadratic and nfs, will you throw away "pseudo smooth" norms in Z?

When one constructs the final squares mod n, one will have to take in account "u", which is with even exponent, so it doesn't affect solving the matrix.
(1) Such norms are extremely rare; They are so extremely rare that they are
not worth worrying about. When a prime in the factor base, other than
the smallest primes (say those less than 10000), divides a norm it
almost always does so to the first power.

(2) Your "pseudo smooth" relation will be found anyway if u is below the large
prime bound. But they are not worth looking for.
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