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.
Thanks very much in advance.