[QUOTE=R.D. Silverman;259599]Read the paper. If you want q(x)^2 = A mod (kN) with A small for
k = 1,2,3, ..... note that every time k changes, you will need a NEW FACTOR
BASE. Computing them is expensive. Also, the final factor base will be
very large since it will be the union of the factor bases for each k.
[/QUOTE]
Not very large but about twice as big, because the factor base includes about half the primes below the bound, so you will have different factor bases but their union will not exceed twice the size of a particular factor base. Anyway I do not think this method can be useful at all.

[QUOTE=alpertron;260263]Not very large but about twice as big, because the factor base includes about half the primes below the bound, so you will have different factor bases but their union will not exceed twice the size of a particular factor base. Anyway I do not think this method can be useful at all.[/QUOTE]

Agreed.