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 Showing results 1 to 25 of 26 Search took 0.01 seconds. Search: Posts Made By: sascha77
 2012-03-26, 21:08 Replies: 95 Views: 24,734 Posted By sascha77 I think the reason why a mersenne number can not... I think the reason why a mersenne number can not expressed as the sum of two squared numbers, is shown in this pdf (On Page 2. Proposition 1) http://www.math.uga.edu/~pete/4400twosquares.pdf...
 2012-03-26, 19:12 Replies: 87 Views: 9,295 Posted By sascha77 Great work !!! I wanted today to check manually... Great work !!! I wanted today to check manually all the factors from the http://mersenne-aries.sili.net site. But you and Dubslow were faster and really found a counterexample. Great. ATH: Can you...
 2012-03-24, 15:00 Replies: 87 Views: 9,295 Posted By sascha77 "...so really all your asking is can 2*m*p+1... "...so really all your asking is can 2*m*p+1 divide 2 Mersennes" Sorry. But I do not quite understand what you mean. Can you give me an example ?
 2012-03-24, 14:43 Replies: 87 Views: 9,295 Posted By sascha77 I see. From what I understand 2^p < 2*k*p^2+1 is... I see. From what I understand 2^p < 2*k*p^2+1 is your break-condition. But you can also set a maximum limit for k direct. Maybe this speeds up the calculation a little bit ? 2^{p} \equiv 1...
 2012-03-24, 13:01 Replies: 87 Views: 9,295 Posted By sascha77 Thanks for the interesting link ! I love such... Thanks for the interesting link ! I love such puzzles. (that are easy to understand, but not so easy to solve) I also have a problem, that has a relation to mersenne numbers. But maybe the...
 Forum: Math 2011-03-14, 23:43 Replies: 43 Views: 4,660 Posted By sascha77 ->When p is composite then 2^{p}-1 can never be... ->When p is composite then 2^{p}-1 can never be prime. Therefore p must be prime so that 2^{p}-1 could be prime. Its because of the factorization. When for example p = a*b, then
 Forum: Math 2011-03-14, 18:36 Replies: 43 Views: 4,660 Posted By sascha77 Thanks. I like your proof. Short and elegant. ... Thanks. I like your proof. Short and elegant. -> Yes the last congruence is unjustified. It must be shown that we can do the f(x)=2*x-1 Operation on both sides. I did this only on the right side...
 Forum: Math 2011-03-09, 18:55 Replies: 43 Views: 4,660 Posted By sascha77 Many thanks for your great help ! Yet I know... Many thanks for your great help ! Yet I know exactly where the (big) failure is. It seems now impossible for me too, to prove that (2^a+2^b) is always co-prime to n.
 Forum: Math 2011-03-09, 14:37 Replies: 43 Views: 4,660 Posted By sascha77 Thanks for the interesting PDF about... Thanks for the interesting PDF about 'miller-rabin test'. I will read that.
 Forum: Math 2011-03-09, 14:26 Replies: 43 Views: 4,660 Posted By sascha77 Yes. That is right. That is exactly what I... Yes. That is right. That is exactly what I meant. Sure I could have done the proof a lot shorter and easier with the multiplikation of (2^{(k)})^{n-1) But the result is the same.
 Forum: Math 2011-03-09, 00:13 Replies: 43 Views: 4,660 Posted By sascha77 I do not know exactly what you mean. Is it... I do not know exactly what you mean. Is it possible that you show me your idea with an example ? thanks.
 Forum: Math 2011-03-09, 00:10 Replies: 43 Views: 4,660 Posted By sascha77 I will now try to proof that if somebody have... I will now try to proof that if somebody have found an composite number n=2^p-1 (with p is prime) so that the congruence 'fails' then it must also fail for all the other a' and b's (with the same n)...
 Forum: Math 2011-03-08, 21:51 Replies: 43 Views: 4,660 Posted By sascha77 I think we do not need to calculate more. ... I think we do not need to calculate more. Because I found out that if someone will find a counterexample with an a and an b so the other a's an b's must also fail for these n=2^p-1 (p prime). And...
 Forum: Math 2011-03-04, 20:00 Replies: 43 Views: 4,660 Posted By sascha77 Thanks !!! Yes it could be that there exist a... Thanks !!! Yes it could be that there exist a counterexample. But nobody knows this until it is found. ;-) A hint: You only need to test a and b to the size of p. this means: test a for a<=p...
 Forum: Math 2011-03-04, 19:07 Replies: 43 Views: 4,660 Posted By sascha77 I noticed that my first post in this topic was... I noticed that my first post in this topic was mathematically not detailled enough and I forgot to mention some assumptions. (Especially that p must always be prime) For this reason I redefine my...
 Forum: Math 2011-03-04, 16:39 Replies: 43 Views: 4,660 Posted By sascha77 OK. my fault. I forgotten to mention that... OK. my fault. I forgotten to mention that mersenne Numbers are Numbers of the Form n = 2^{p}-1 with: The variable p is prime !!!!! If the mersenne number n with n=2^{p}-1 is also prime then...
 Forum: Math 2011-03-04, 16:29 Replies: 43 Views: 4,660 Posted By sascha77 No. This is false. set p=11 ->n=2^{p}-1 =... No. This is false. set p=11 ->n=2^{p}-1 = 2047 for this: (2^{11}+2^{1})^{2046} \equiv (\;(2^{11} + 2^{1})\;mod(\;2047)\;)^{2046} \equiv 3^{2046} \equiv 1013\;(mod\; 2047)
 Forum: Math 2011-03-04, 02:44 Replies: 43 Views: 4,660 Posted By sascha77 I think you did not read carefully what i wrote... I think you did not read carefully what i wrote or my english grammar was too bad. Let me show you what I did and what i meant: I played with the Lemma : (X-a)^n \equiv\; (X^n -a) \;(mod...
 Forum: Math 2011-03-04, 01:03 Replies: 43 Views: 4,660 Posted By sascha77 I think you did really a mistake.:smile: 2^x... I think you did really a mistake.:smile: 2^x - 2^{(x-z)} = 2^x - \frac{2^x}{2^z} = \frac{2^x*(2^z-1)}{2^z}
 Forum: Math 2011-03-03, 23:02 Replies: 43 Views: 4,660 Posted By sascha77 Question about a mersenne-number property I discovered a nice property about mersenne numbers. (2^a+2^b)^{n}\equiv 2^a + 2^b\; (mod\; n) When n=2^{p}-1 is not prime then this is true only for the two trivial cases: 1.) a = b ...
 Forum: Math 2010-05-07, 06:08 Replies: 15 Views: 2,536 Posted By sascha77 Hello Silverman, Yes i mean that p must be Prime.... Hello Silverman, Yes i mean that p must be Prime. M_p is the abbreviation of Mersenne-number with p prime. Thank you, that you showed me, that Proposition 1 is trivial. But it was not the...
 Forum: Math 2010-04-25, 23:31 Replies: 15 Views: 2,536 Posted By sascha77 Explanation of my conjecture. Hello , I wrote an PDF-document to show why I am interested that "my" conjecture is true. Sorry that it took so long time ;-( In this PDF there might be some "new" Mersenne Properties, but ...
 Forum: Math 2010-01-08, 08:44 Replies: 15 Views: 2,536 Posted By sascha77 Thanks maxal, Now I see the connection to... Thanks maxal, Now I see the connection to the Wieferich primes and I feel confident now that this is hard to solve.
 Forum: Math 2010-01-07, 08:13 Replies: 15 Views: 2,536 Posted By sascha77 Mersenne Conjecture Hello, My conjecture is : Let 2^p-1 be an Mersenne-number, and a is an element from 2^p-1 (1)\:\: a^{(p*p)} \equiv 1\: (mod\: 2^p-1)
 Forum: Math 2010-01-07, 08:06 Replies: 2 Views: 1,055 Posted By sascha77 ok. thanks. I will post this in the gimps->math... ok. thanks. I will post this in the gimps->math Forum
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