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2012-05-31, 10:03
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#1 |
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May 2012
22 Posts |
help on FFT in Z/mZ
Hi,
I have just subscribed to this mailing-list even if I am very interested in primes search. I intend to write a program to find prime Mersenne numbers using Lucas-Lehmer test and FFT in Z/mZ (the ring of integers modulo an prime integer m). I need some documentation on how to find a primitive root of unity andFind all n-th roots of unity in Z*p (arithmetic is mod p) . |
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2012-05-31, 11:51
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#2 |
"Nancy"
Aug 2002
Alexandria
2,467 Posts |
Try a = 2, 3, 5, 6, 7, 10, ... (non-powers) (mod p) and test that for each prime q | p-1, a([I]p[/I]-1)/[I]q[/I] != 1 (mod p). Then, and only then, is a a primitive root modulo p. To get a primitive n-th root r modulo p, where n | p-1, use r = a([I]p[/I]-1)/[I]n[/I] (mod p).
Last fiddled with by akruppa on 2012-05-31 at 18:35 |
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2012-05-31, 12:03
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#3 |
Jun 2003
117328 Posts |
Googling "Number theoretic transform" might help.
EDIT:- So not a mailing list. Last fiddled with by axn on 2012-05-31 at 12:04 |
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2012-05-31, 17:34
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#4 | |
"Lucan"
Dec 2006
England
2·3·13·83 Posts |
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2012-05-31, 17:35
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#5 | |
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Bamboozled!
"πΊππ·π·π"
May 2003
Down not across
22×5×72×11 Posts |
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2012-05-31, 19:27
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#6 | |
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If I May
"Chris Halsall"
Sep 2002
Barbados
976710 Posts |
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2012-05-31, 23:19
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#7 | |
"Gang aft agley"
Sep 2002
2·1,877 Posts |
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2012-06-01, 05:39
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#8 | |
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Bamboozled!
"πΊππ·π·π"
May 2003
Down not across
22·5·72·11 Posts |
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2012-06-01, 08:36
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#9 | |
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May 2012
410 Posts |
Quote:
thank for your feedback but I didn't understand what you mean by mailing list |
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2012-06-01, 08:49
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#10 | |
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Bamboozled!
"πΊππ·π·π"
May 2003
Down not across
22·5·72·11 Posts |
Quote:
"Mail" has several meanings in English. As well as a form of written communication, mail is also a type of armour. Chainmail armour is a network of interlinked metal rings attached to some backing material, traditionally either leather or woollen cloth. Platemail is made from solid sheets of metal, usually held together and onto the wearer by leather straps. A ring, as you doubtless know, is a specific mathematical object. Z/mZ is a ring in this sense. Further wordplay there. Finally (though first in the thread) "mail" and "male" are pronounced the same in English and although femail isn't really an English word it is very often seen. Apologies if this is teaching you stuff you already know but I doubt you're the only person here whose first language is not English. Paul |
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2012-06-01, 10:18
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#11 | |
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May 2012
1002 Posts |
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Thank you. but how to use mailing list, plating list, OP,... to find all n-th roots of unity. please if you have any link or website . |
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