mersenneforum.org  

Go Back   mersenneforum.org > Search Forums

Showing results 1 to 25 of 26
Search took 0.01 seconds.
Search: Posts Made By: sascha77
Forum: Other Mathematical Topics 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...
Forum: Other Mathematical Topics 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...
Forum: Other Mathematical Topics 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 ?
Forum: Other Mathematical Topics 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...
Forum: Other Mathematical Topics 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
Showing results 1 to 25 of 26

 
All times are UTC. The time now is 14:16.


Fri Aug 19 14:16:02 UTC 2022 up 1 day, 11:44, 1 user, load averages: 1.67, 1.57, 1.53

Powered by vBulletin® Version 3.8.11
Copyright ©2000 - 2022, Jelsoft Enterprises Ltd.

This forum has received and complied with 0 (zero) government requests for information.

Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation.
A copy of the license is included in the FAQ.

≠ ± ∓ ÷ × · − √ ‰ ⊗ ⊕ ⊖ ⊘ ⊙ ≤ ≥ ≦ ≧ ≨ ≩ ≺ ≻ ≼ ≽ ⊏ ⊐ ⊑ ⊒ ² ³ °
∠ ∟ ° ≅ ~ ‖ ⟂ ⫛
≡ ≜ ≈ ∝ ∞ ≪ ≫ ⌊⌋ ⌈⌉ ∘ ∏ ∐ ∑ ∧ ∨ ∩ ∪ ⨀ ⊕ ⊗ 𝖕 𝖖 𝖗 ⊲ ⊳
∅ ∖ ∁ ↦ ↣ ∩ ∪ ⊆ ⊂ ⊄ ⊊ ⊇ ⊃ ⊅ ⊋ ⊖ ∈ ∉ ∋ ∌ ℕ ℤ ℚ ℝ ℂ ℵ ℶ ℷ ℸ 𝓟
¬ ∨ ∧ ⊕ → ← ⇒ ⇐ ⇔ ∀ ∃ ∄ ∴ ∵ ⊤ ⊥ ⊢ ⊨ ⫤ ⊣ … ⋯ ⋮ ⋰ ⋱
∫ ∬ ∭ ∮ ∯ ∰ ∇ ∆ δ ∂ ℱ ℒ ℓ
𝛢𝛼 𝛣𝛽 𝛤𝛾 𝛥𝛿 𝛦𝜀𝜖 𝛧𝜁 𝛨𝜂 𝛩𝜃𝜗 𝛪𝜄 𝛫𝜅 𝛬𝜆 𝛭𝜇 𝛮𝜈 𝛯𝜉 𝛰𝜊 𝛱𝜋 𝛲𝜌 𝛴𝜎𝜍 𝛵𝜏 𝛶𝜐 𝛷𝜙𝜑 𝛸𝜒 𝛹𝜓 𝛺𝜔