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Old 2005-08-08, 18:30   #7
Mar 2005

438 Posts

Originally Posted by R.D. Silverman
Define "close". What you suggest is certainly not trivial.

As for writing a program, I suspect you have not considered alll of
the ramifications. What polynomial would you choose for (say)
2, 1450L?
Hey, you are the master of poly selection! You tell me! :)

OK, seriously: I was only thinking about rather simple cases (at least in the beginning), for numbers like k*x^p+c. The program should make a few tests (about presence of Aurfeillian factors, for example), and try to compute some polynomials, and present the one with smallest coefficents. There are some tricks to do, and beginner not always can see it, and even more advanced (but still amateur) can miss, or simply miscalculate. (I can for sure).
Simple example from ggnfs doc: for N=16*10^143-1 obvious poly could be f(x)=4*x^5-25, but a slightly less obvious would be f(x)=x^5-200. Newbie can easily miss this, and amateur should check if his poly is good enough. (Experts can manage by themselves.) :)

As for program checking for "closeness" of N to some multiple of some power of some number :), I also would ask you about advice, what "closeness" condition should be. I thought about range of k,c<10^((logN)/10), so for n=10^120 cutoff point would be at 10^12.

For now, I have got mainly ideas, and want to listen what others are thinking and advicing. If someone wants to write such a program, you are very welcome, I am not good at it.


Last fiddled with by Washuu on 2005-08-08 at 18:40
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