Quote:
Originally Posted by baih
Let Mersenne number 2^{n} 1
if 2^{n} 1 composite
2^{n} 1 = n^{2}xy + (x+y)n + 1
so 2^{n} /n
= (n^{2}xy + (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
2^{11}1 = 2047
(20471) /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 bruteforce (trying different integers for a solution) and the combinations are astronomically large.
You might have some fun with WolframAlpha:
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 thinkingpower in the process.