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Old 2020-08-20, 20:47   #1
baih
 
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Jun 2019

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Default 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
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