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Search: Posts Made By: jfollas
Forum: Lounge 2005-03-06, 16:38
Replies: 43
Views: 2,924
Posted By jfollas
29619697

29619697
Forum: Math 2004-09-11, 12:51
Replies: 37
Views: 4,431
Posted By jfollas
What stuck in my mind was that when you multiply...

What stuck in my mind was that when you multiply using FFT, you first represent the number as a polynomial equation:

57829 = 5x^4 + 7x^3 + 8x^2 + 2x + 9

I wasn't sure if the roots of such an...
Forum: Math 2004-09-10, 14:18
Replies: 37
Views: 4,431
Posted By jfollas
General Solution to Polynomial Equations

What are the implications for factoring/primality testing (if any) of the newly announced general solution to polynomial equations? This piqued my interest because I remembered something about FFT...
Forum: Miscellaneous Math 2004-08-18, 15:45
Replies: 16
Views: 1,796
Posted By jfollas
Well, that's an important discovery that I made...

Well, that's an important discovery that I made earlier this year and have been developing ever since.... I call this "Shortcutting the Lucas-Lehmer Test" because all you need to do is prove that...
Forum: Math 2004-08-01, 19:07
Replies: 3
Views: 836
Posted By jfollas
I've studied the Lucas-Lehmer sequence quite a...

I've studied the Lucas-Lehmer sequence quite a bit over the past year, and based on all of the empirical evidence that I've collected, I have concluded that the LL sequence will zero out after any...
Forum: Math 2004-08-01, 12:12
Replies: 3
Views: 836
Posted By jfollas
The LL test will zero out for a prime number Mp...

The LL test will zero out for a prime number Mp on step P-1 if the starting term is from the sequence:

A(0)=4, A(1)=52, A(n)=(14*A(n-1) - A(n-2)) mod Mp [Sloane A018844]

It is possible that...
Forum: Software 2004-07-31, 14:51
Replies: 27
Views: 3,923
Posted By jfollas
Common question... Depends what step you're on. ...

Common question... Depends what step you're on.

In the beginning, Prime95 tries to find small factors of the prime using several different methods. If a small factor is found, then Prime95...
Forum: Math 2004-07-30, 15:11
Replies: 61
Views: 45,065
Posted By jfollas
Is there a FFT implementation that would be...

Is there a FFT implementation that would be better suited for repeatedly performing the multiplication step while remaining in the transform (i.e., where precision errors are not an issue), or at...
Forum: Math 2004-07-30, 02:44
Replies: 2
Views: 1,190
Posted By jfollas
Check out Dario Alpern's "Generic Two Integer...

Check out Dario Alpern's "Generic Two Integer Variable Equation Solver":

http://www.alpertron.com.ar/QUAD.HTM

He offers a lot of background information about this subject.

BTW: You might not...
Forum: Math 2004-07-29, 13:58
Replies: 61
Views: 45,065
Posted By jfollas
I'm still trying to get my head around...

I'm still trying to get my head around multiplying using FFT's, but I have a couple questions that popped up:

As I understand, to multiply using FFT, you need to do a transform, perform the...
Forum: Math 2004-07-21, 17:45
Replies: 7
Views: 2,104
Posted By jfollas
I apologize if this is repeated information, but...

I apologize if this is repeated information, but I haven't specifically seen it posted anywhere.


I did some studying of the "roots of LLT", specifically around Sloane's A018844:
...
Forum: Math 2004-07-02, 22:26
Replies: 3
Views: 1,051
Posted By jfollas
Hmm, it seems that your explaination works great...

Hmm, it seems that your explaination works great for the case where the modulus is less than the exponent as in the example 37^1024 (mod 127). Thanks for the details, since I haven't seen that...
Forum: Math 2004-07-02, 22:01
Replies: 3
Views: 1,051
Posted By jfollas
By Mersenne, I simply meant any number in the...

By Mersenne, I simply meant any number in the form of 2^P-1, be it a prime or composite (though primality not necessarily known at the evaluation time).
Forum: Math 2004-07-02, 13:18
Replies: 3
Views: 1,051
Posted By jfollas
Raising numbers to a power of two

Are there any shortcuts for raising a number to a power of two (modulo a mersenne)?

Examples:

37^1024 (mod 127)

65^2048 (mod 8191)

I realize that the exponential operation using the...
Showing results 1 to 14 of 14

 
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