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Old 2020-08-21, 03:42   #7
a1call's Avatar
"Rashid Naimi"
Oct 2015
Remote to Here/There

3·733 Posts

Originally Posted by baih View Post
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


211-1 = 2047
(2047-1) /2= 186

186 = nxy+x+y
= 11* 8*2 + 8+2
X= 8
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:

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