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 Showing results 1 to 25 of 1000 Search took 0.14 seconds. Search: Posts Made By: alpertron
 Forum: Factoring 2021-04-03, 15:59 Replies: 5 Views: 1,745 Posted By alpertron Solving Diophantine equations of second degree on... Solving Diophantine equations of second degree on two variables requires integer factorization. For example: find the integer solutions (x, y) of a circle represented by x2 + y2 = N where N is a...
 Forum: Data 2021-03-29, 12:14 Replies: 378 Views: 58,339 Posted By alpertron The speed of srbase depends also on how many... The speed of srbase depends also on how many users donate GPU time to the trial factoring project. According to https://srbase.my-firewall.org/sr5/server_status.php , there are 121 active users,...
 Forum: Programming 2021-03-02, 01:53 Replies: 38 Views: 14,312 Posted By alpertron There were several buffer overflows that I've... There were several buffer overflows that I've just fixed during this week. Now it works.
 Forum: Miscellaneous Math 2021-01-24, 16:14 Replies: 2 Views: 550 Posted By alpertron I've just tested the first sentence written by... I've just tested the first sentence written by the OP with values of x up to 10 million using the following line in PARI-GP: for (x=2,10000000,n=x^3-x-1;if (Mod(x,n)^n==Mod(x,n) &&...
 Forum: Programming 2020-12-25, 19:05 Replies: 38 Views: 14,312 Posted By alpertron You are right. But the Eisenstein criterion... You are right. But the Eisenstein criterion cannot be used for all polynomials. There is still more room for optimization.
 Forum: Programming 2020-12-25, 18:21 Replies: 38 Views: 14,312 Posted By alpertron I've just added FFT for modular polynomial... I've just added FFT for modular polynomial multiplications when the modulus is small. This enables faster factoring when trying to factor integer polynomials, especially when the number of modular...
 Forum: Programming 2020-12-13, 21:06 Replies: 38 Views: 14,312 Posted By alpertron I've just added TeX output to my polynomial... I've just added TeX output to my polynomial factorization calculator located at https://www.alpertron.com.ar/POLFACT.HTM For example, the roots of x17 + 1 are: \begin{array}{l}...
 Forum: Programming 2020-11-30, 17:15 Replies: 38 Views: 14,312 Posted By alpertron I should add TEX output to my calculators when... I should add TEX output to my calculators when requested by user. That would be an interesting addition to the programs.
 Forum: Programming 2020-11-30, 15:47 Replies: 38 Views: 14,312 Posted By alpertron There is a copy error. Using your input I get: ... There is a copy error. Using your input I get: x1 to x3 = 0 r = (19 + 3 * 33^(1/2))^(1/3) s = (19 - 3 * 33^(1/2))^(1/3) x4 = 1 + r + s x5 = 1 - (r + s) / 2 + (i/2) * (r - s) * 3^(1/2) x6 =...
 Forum: Programming 2020-11-28, 23:13 Replies: 38 Views: 14,312 Posted By alpertron I fixed the LLL routine and optimized the Hensel... I fixed the LLL routine and optimized the Hensel Lifting. Now the factorization of polynomials of degree less than 1000 with small coefficients can be done in seconds.
 Forum: Data 2020-11-26, 02:28 Replies: 6 Views: 1,546 Posted By alpertron Thanks. So this was a false alarm. Thanks. So this was a false alarm.
 Forum: Data 2020-11-26, 01:06 Replies: 6 Views: 1,546 Posted By alpertron Too few factors found in 600M to 620M I've just looked at https://www.mersenne.ca/status/tf/0/1/2/60000 and I found that there should be some hardware error: 21192 factors in the range 600M-610M today in the 72-bit range: only 3...
 2020-10-17, 02:44 Replies: 3 Views: 1,226 Posted By alpertron Computing the Jacobi symbol is a lot faster than... Computing the Jacobi symbol is a lot faster than modular exponentiation. This is the source code I wrote in C language based on Crandall's and Pomerance's Prime Number book: // Calculate...
 Forum: Programming 2020-10-04, 21:20 Replies: 38 Views: 14,312 Posted By alpertron When the irreducible polynomial has degree >= 5,... When the irreducible polynomial has degree >= 5, now my code performs the factorization of this polynomials with prime modulus up to 100. If the conditions of Keith Conrad's paper that you can...
 Forum: FermatSearch 2020-10-03, 18:15 Replies: 65 Views: 7,785 Posted By alpertron Before even thinking on performing the primality... Before even thinking on performing the primality check of F33, a lot more trial factoring is needed and then someone has to run P-1.
 Forum: Programming 2020-10-02, 19:42 Replies: 38 Views: 14,312 Posted By alpertron All these examples are working now. Thanks for... All these examples are working now. Thanks for finding the errors. Please refresh the page to get the current version.
 Forum: Programming 2020-10-02, 01:18 Replies: 38 Views: 14,312 Posted By alpertron I fixed this error. Please refresh the page and... I fixed this error. Please refresh the page and retry. Since the application works with integer polynomials, the slash operator performs the division disregarding the remainder. This means...
 Forum: Programming 2020-10-01, 18:32 Replies: 38 Views: 14,312 Posted By alpertron I've just fixed this error. Please refresh the... I've just fixed this error. Please refresh the page so the Web page is dated 1 October 2020 and try again.
 Forum: Programming 2020-09-30, 03:40 Replies: 38 Views: 14,312 Posted By alpertron Now the response of the Web application is... Now the response of the Web application is shorter for polynomials of the form x5+n (n = integer).
 Forum: Programming 2020-09-30, 02:53 Replies: 38 Views: 14,312 Posted By alpertron The values found by the solver are correct as you... The values found by the solver are correct as you can see by unsetting pretty print, and then factoring it again. This is the output of the calculator. R1 = 0 R2 = (15625)^(1/5) R3 = 0 R4...
 Forum: Programming 2020-09-27, 22:47 Replies: 38 Views: 14,312 Posted By alpertron Hello folks, I have added more features to... Hello folks, I have added more features to this calculator at https://www.alpertron.com.ar/POLFACT.HTM Now it quickly factors integer polynomials with degree up to 1000 using Van Hoeij...
 Forum: Factoring 2020-09-25, 03:28 Replies: 40 Views: 17,169 Posted By alpertron I've just updated the page... I've just updated the page https://www.alpertron.com.ar/BRILLIANT3.HTM with your results. Thanks a lot.
 Forum: Factoring 2020-09-19, 00:24 Replies: 40 Views: 17,169 Posted By alpertron I've just added the discoveries posted to this... I've just added the discoveries posted to this thread to https://www.alpertron.com.ar/BRILLIANT.HTM and also fixed the errors detected at https://www.alpertron.com.ar/BRILLIANT2.HTM
 Forum: Factoring 2020-09-13, 17:02 Replies: 40 Views: 17,169 Posted By alpertron At this moment I'm making changes to my... At this moment I'm making changes to my calculator that factors and finds the roots of polynomials (you can see it at https://www.alpertron.com.ar/POLFACT.HTM). After that, I will update the page of...
 Forum: Lounge 2020-08-26, 14:44 Replies: 48 Views: 12,234 Posted By alpertron In Argentina merchants are required to indicate... In Argentina merchants are required to indicate the price per kg or liter, so this cheat cannot be done.
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