mersenneforum.org Mersenne factorization by (nxy+x+y)
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 2020-08-20, 20:47 #1 baih     Jun 2019 2216 Posts Mersenne factorization by (nxy+x+y) Let Mersenne number 2n -1 if 2n -1 composite 2n -1 = n2xy + (x+y)n + 1 so 2n /n = (n2xy + (x+y)n) /n = nxy+x+y Finding the x and y we can factor the number into a product (nx)+1 and (ny)+1 example 211-1 = 2047 (2047-1) /2= 186 186 = nxy+x+y = 11* 8*2 + 8+2 X= 8 Y=2 and 2047 = (88+1)*(22+1) Difficulty and complexity (nxy+x+y) like a Diophantine equation Are there any solutions? sory for my english
 2020-08-20, 22:20 #2 Viliam Furik   Jul 2018 Martin, Slovakia 229 Posts Obvious mistakes I would like to point out a few mistakes. 1. (2^n) is never divisible by (n), (2^n-2) is divisible by (n), when (n) is prime (btw, it is because of Little Fermat theorem) 2. (2047-1) /2= 186; you probably meant (2047-1)/11 = 186. Apart from these typos, I guess I will leave the topic for other guys.
2020-08-20, 22:27   #3
baih

Jun 2019

1000102 Posts

Quote:
 Originally Posted by Viliam Furik I would like to point out a few mistakes. 1. (2^n) is never divisible by (n), (2^n-2) is divisible by (n), when (n) is prime (btw, it is because of Little Fermat theorem) 2. (2047-1) /2= 186; you probably meant (2047-1)/11 = 186. Apart from these typos, I guess I will leave the topic for other guys.
thanks i mean (2^n)-2

Last fiddled with by baih on 2020-08-20 at 22:29

 2020-08-21, 00:38 #4 Batalov     "Serge" Mar 2008 Phi(4,2^7658614+1)/2 23·7·163 Posts Please demonstrate the power of this method on a tiny number 2^1277-1. it is composite. Show us.
2020-08-21, 01:09   #5
baih

Jun 2019

2×17 Posts

Quote:
 Originally Posted by Batalov Please demonstrate the power of this method on a tiny number 2^1277-1. it is composite. Show us.
non

The difficulty is the same as the difficulty of (Trial division)
But it may help in some cases

If someone found a solution to the equation c=nxy+x+y

Last fiddled with by baih on 2020-08-21 at 01:17

2020-08-21, 03:21   #6
mathwiz

Mar 2019

10410 Posts

Quote:
 Originally Posted by baih If someone found a solution to the equation c=nxy+x+y
There's infinitely many solutions: c=x=y=0, x=y=1 and c=n+2, and so on.

What is the purpose of this is equation and what constraints are you placing on the variables?

2020-08-21, 03:42   #7
a1call

"Rashid Naimi"
Oct 2015
Remote to Here/There

1,931 Posts

Quote:
 Originally Posted by baih Let Mersenne number 2n -1 if 2n -1 composite 2n -1 = n2xy + (x+y)n + 1 so 2n /n = (n2xy + (x+y)n) /n = nxy+x+y Finding the x and y we can factor the number into a product (nx)+1 and (ny)+1 example 211-1 = 2047 (2047-1) /2= 186 186 = nxy+x+y = 11* 8*2 + 8+2 X= 8 Y=2 and 2047 = (88+1)*(22+1) Difficulty and complexity (nxy+x+y) like a Diophantine equation Are there any solutions? sory for my english
That's a good find. I think I have a similar post here somewhere.

The problem is you need brute-force (trying different integers for a solution) and the combinations are astronomically large.

You might have some fun with Wolfram-Alpha:

https://www.wolframalpha.com/input/?...er+the+integer

https://www.wolframalpha.com/input/?...er+the+integer

Good luck, try expanding the concept. You might get something interesting or at worst expand your thinking-power in the process.

2020-08-25, 07:55   #8
LaurV
Romulan Interpreter

Jun 2011
Thailand

22·7·317 Posts

Quote:
 Originally Posted by a1call I think I have a similar post here somewhere.
Except your post was left-aligned, therefore easier to read, haha. This is just some rubbish thrown in the middle of the screen, impossible to read.

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