Author 
Comment/Response 
Piers

06/18/06 3:57pm
Hi
I would very much appreciate some help with this problem.
I am looking at defactoring p*p with the difference of squares method. Essentially when the integer values for X^2  x^2 = pp are found one can deduce from the values of x and X, p and p with a few simple calculations.
The problem which I have difficulties with is getting the formula to work in Mathematica. Essentially I am looking for this kind of format.
Mod[X^2 + 46X + 48, x^2]
The basic problem here is that if the list lenghts of X and x values are the same Mathematica divides the X=1 result by x=1 result.
I would like the whole of the range of x into X =1, then the whole range of x into X=2 and so forth.
Now I am actually working with large numbers and I also need a filter ideally just to return the integers and the values of X and x for those values.
I am sorry it is such a lot to ask but I have been through most of the Mathematica book trying to answer this one and do not feel close the answer.
I guess some variety of looping through getting x one value higher each time may be the answer??? I have not done programming before so am in deep water!
If you are interested this is an extension of Fermat and further details can be found here.
http://www.ams.org/mcom/199968228/S0025571899011333/S0025571899011333.pdf
Thanks very much in advance.
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