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 Showing results 1 to 8 of 8 Search took 0.00 seconds. Search: Posts Made By: LaurV
 Forum: science_man_88 2013-09-25, 05:45 Replies: 396 Views: 41,338 Posted By LaurV you don't really need to use the \times sign, you... you don't really need to use the \times sign, you better use a "\ " (backslash space) there, or if you really need to use a sign, then use \cdot. Those "x"-es make the formulas very difficult to read.
 Forum: science_man_88 2011-11-18, 16:17 Replies: 396 Views: 41,338 Posted By LaurV I know that, and this was the cause for my first... I know that, and this was the cause for my first error, when I said that we can not compute the square root mod a 4k+1 prime. The point is that given a prime p, half of the values mod p are QR,...
 Forum: science_man_88 2011-11-18, 15:04 Replies: 396 Views: 41,338 Posted By LaurV Does "no problem" means "without factoring n=p*q... Does "no problem" means "without factoring n=p*q into p and q"? I think you can not. Excluding taking all residues from 2 to n and try them. That is brute force. Try computing sqrt(2) mod M1061,...
 Forum: science_man_88 2011-11-18, 09:27 Replies: 396 Views: 41,338 Posted By LaurV I don't know any, without factoring the composite... I don't know any, without factoring the composite number. End even that, to take square roots modulo a prime, I think there are known algorithms only when the prime is 3 mod 4 (not sure about it, but...
 Forum: science_man_88 2011-11-18, 08:31 Replies: 396 Views: 41,338 Posted By LaurV Yes, the last one. He should check first if the... Yes, the last one. He should check first if the number is perfect square. Theoretically, sqrt(Mod(3,35)) does not exists, as 3 is not a QR mod 5 or mod 7. And that is why you can not extract sqrt of...
 Forum: science_man_88 2011-11-18, 05:35 Replies: 396 Views: 41,338 Posted By LaurV ok, it is about the same story, the improvement... ok, it is about the same story, the improvement is that you skip SG primes (why I did not think to it??) but on the other hand you compute 2^n three times and by a slower method (pari uses...
 Forum: science_man_88 2011-11-17, 05:45 Replies: 396 Views: 41,338 Posted By LaurV Yarrr! :sirrobin:I didn't know that! Now after... Yarrr! :sirrobin:I didn't know that! Now after reading, it sounds logical. However the "factoring the number" part stays, and what I said is common sense: if we could compute sigma without factoring...
 Forum: science_man_88 2011-11-17, 03:05 Replies: 396 Views: 41,338 Posted By LaurV The sigma function is factoring the number first.... The sigma function is factoring the number first. There is no other way to compute it. It would take a longer amount of time to compute sigma(x) than it would take to factor x, especially if x has a...
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