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Forum: Computer Science & Computational Number Theory 2013-03-15, 13:30
Replies: 40
Views: 3,575
Posted By Gammatester
The summands of his series are (-1)^n/a_n, in...

The summands of his series are (-1)^n/a_n, in this case (-1)^(n+1)*(n+1), i.e -1 + 2 - 3 ....
Forum: Computer Science & Computational Number Theory 2013-03-15, 13:04
Replies: 40
Views: 3,575
Posted By Gammatester
As often you are either wrong or do not cite...

As often you are either wrong or do not cite correctly. Take an = -1/(n+1) ; then an < an+1 and the limit is zero, but obviously the series is not convergent.
Forum: Miscellaneous Math 2013-01-31, 08:19
Replies: 9
Views: 826
Posted By Gammatester
How do you get the starting value r1 := r with...

How do you get the starting value r1 := r with r^2 = -1 mod m without taking square roots mod m?
Forum: Math 2012-05-23, 12:47
Replies: 13
Views: 1,406
Posted By Gammatester
Either you have not completely specified your...

Either you have not completely specified your generalised conjecture or there is a counter example for Case I! Take a=-2 and c=-9. Then gcd(a,c)=1 but there are at least two solutions for (x,n):
...
Forum: Homework Help 2012-05-16, 13:30
Replies: 7
Views: 1,596
Posted By Gammatester
If n= p_1 \times p_2 \times \cdots \times p_k is...

If n= p_1 \times p_2 \times \cdots \times p_k is square-free, then Z/n Z is isomorphic to the product of fields Z/p_1 Z \times Z/p_2 Z \times \cdots \times Z/p_k Z. So if "the result is clear for n...
Forum: Homework Help 2012-05-16, 07:41
Replies: 7
Views: 1,596
Posted By Gammatester
With n=8; x=Mod(4,n); y=Mod(1,n); z=Mod(2,n) you...

With n=8; x=Mod(4,n); y=Mod(1,n); z=Mod(2,n) you have x^2*y = x^2*z = Mod(0, 8) but x*y = Mod(4, 8) != x*z = Mod(0, 8).
Forum: Miscellaneous Math 2012-05-14, 11:28
Replies: 3
Views: 416
Posted By Gammatester
You can start with a newer version, the page you...

You can start with a newer version, the page you reference is almost five years old!

There is a free pdf version of Stein's "Elementary Number Theory" at http://sage.math.washington.edu/ent/ and...
Forum: Math 2012-03-20, 15:43
Replies: 15
Views: 1,895
Posted By Gammatester
Depends on the exact implementation, but I guess...

Depends on the exact implementation, but I guess from the description that it includes the BPSW test. For this test there are no known counter-examples. See http://www.trnicely.net/misc/bpsw.html and...
Forum: Other Mathematical Topics 2012-03-15, 09:56
Replies: 95
Views: 19,673
Posted By Gammatester
You should not change your questions after they...

You should not change your questions after they have been answered. My post handles the task: Decompose p = 3 mod 8 into p = x^2 + 2 y^2. And computing the modular square root mod p of this form is...
Forum: Other Mathematical Topics 2012-03-15, 08:49
Replies: 95
Views: 19,673
Posted By Gammatester
Use Cornacchia's algorithm (see...

Use Cornacchia's algorithm (see http://en.wikipedia.org/wiki/Cornacchia%27s_algorithm or Crandall/Pomerance, Algorithm 2.3.12), it is very effective.
Forum: science_man_88 2011-11-18, 17:24
Replies: 396
Views: 27,951
Posted By Gammatester
My formulation was a be misleading, I wanted to...

My formulation was a be misleading, I wanted to say: If the you know the prime decomposition of n then are not hard problems to compute sqrt(a) mod n. If you do not know it you can say that a is a...
Forum: science_man_88 2011-11-18, 10:42
Replies: 396
Views: 27,951
Posted By Gammatester
There is no problem to compute sqrt(x) mod p*q or...

There is no problem to compute sqrt(x) mod p*q or sqrt(x) mod p^k with p,q prime if x is a quadratic residue mod p and mod q.

IMHO the hard case is if the Jacobi symbol (x | p*q) is 1, e.q. (3 |...
Forum: science_man_88 2011-11-18, 09:06
Replies: 396
Views: 27,951
Posted By Gammatester
I see. But I wonder what to do with e.g....

I see. But I wonder what to do with e.g. sqrt(Mod(29,35))? Is there a systematic approach to get the solutions 8,13,22,27 mod 35?
Forum: science_man_88 2011-11-18, 08:02
Replies: 396
Views: 27,951
Posted By Gammatester
What version of pari/gp? Can you give an example?...

What version of pari/gp? Can you give an example? Versions 2.3.4 and 2.4.2 give the correct root Mod(3,x) for sqrt(Mod(9,x)) for quick tests with x=17,19,101 even though 3 is not a quadratic residue...
Forum: Computer Science & Computational Number Theory 2011-11-09, 14:28
Replies: 171
Views: 15,337
Posted By Gammatester
You should add another line to include the twin...

You should add another line to include the twin (3,5) :smile:
Forum: Programming 2011-08-24, 08:56
Replies: 5
Views: 761
Posted By Gammatester
As usual you are far too vague for a precise...

As usual you are far too vague for a precise direct answer.

First of all: Do you want to test multi-precision numbers or single precision numbers (for single precision in the FPU range a simple...
Forum: Computer Science & Computational Number Theory 2011-08-23, 08:55
Replies: 66
Views: 11,699
Posted By Gammatester
Perhaps your processor is clever and does an...

Perhaps your processor is clever and does an optimization you obviously refuse! Why do you choose this S? The largest factor is 11969 (much smaller than your first), and thus it is no surprise that...
Forum: Computer Science & Computational Number Theory 2011-08-23, 07:33
Replies: 66
Views: 11,699
Posted By Gammatester
Any time for the original problem of...

Any time for the original problem of JohnFullspeed for 10000000# mod 50847533 that is greater than say 1 ms, shows that used implementation is bad: Since 50847533 = 11*31*149113, the result is zero...
Forum: Math 2011-07-19, 12:55
Replies: 2
Views: 728
Posted By Gammatester
[\log_2(n)] if your number is n, i.e. for a 20...

[\log_2(n)] if your number is n, i.e. for a 20 decimal digit number [\log_2(10^{20}-1)] = 66. If you want different prime factors, search the largest product of the first primes that is <= n and...
Forum: Miscellaneous Math 2011-07-07, 14:36
Replies: 45
Views: 3,089
Posted By Gammatester
Since ldesnogu assumes a power of two base, I...

Since ldesnogu assumes a power of two base, I cannot see how you can be faster with your log_2 approach. If the most significant limb has a popcount > 1 both algorithms will have the result "No power...
Forum: Miscellaneous Math 2011-07-05, 09:50
Replies: 61
Views: 4,291
Posted By Gammatester
Yes, there is a Karatsuba square root algorithm:...

Yes, there is a Karatsuba square root algorithm: P. Zimmermann, Karatsuba Square Root, INRIA Research Report RR-3805 (http://hal.inria.fr/inria-00072854/en/) (http://hal.inria.fr/inria-00072854/en/)
Forum: Miscellaneous Math 2011-07-04, 21:22
Replies: 61
Views: 4,291
Posted By Gammatester
The reason why RSA problems above say 512 bit...

The reason why RSA problems above say 512 bit numbers are difficult, is not caused by timing problems of the arithmetic. They are essentially difficult because integer factorization is difficult in...
Forum: Miscellaneous Math 2011-07-04, 15:00
Replies: 61
Views: 4,291
Posted By Gammatester
IMO you are too much focused on 32/64 bit Intel...

IMO you are too much focused on 32/64 bit Intel arithmetic (see e.g. the BSR instruction). As others have already said, your pseudo code looks like O(n^2).

Do you have implemented your code for...
Forum: Miscellaneous Math 2011-06-22, 13:27
Replies: 39
Views: 2,138
Posted By Gammatester
You should address this question to...

You should address this question to JohnFullspeed. That's why I said he should specify what he wants to do. Maybe he wants to compute \sigma_0. But even then the test should be: if j>2 then output...
Forum: Miscellaneous Math 2011-06-22, 12:51
Replies: 39
Views: 2,138
Posted By Gammatester
IMHO it is bad practice to change large parts of...

IMHO it is bad practice to change large parts of a post after someone had already answered. But your new code seems even more nonsense. If my knowledge of the French language is not completely wrong,...
Showing results 1 to 25 of 38

 
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