View Single Post
Old 2020-09-12, 01:09   #3
Dr Sardonicus
 
Dr Sardonicus's Avatar
 
Feb 2017
Nowhere

2×1,949 Posts
Default

Quote:
Originally Posted by bhelmes View Post
If f | Mp and p is prime then

a) f | 2n²-1

b) but not f=2n²-1


a) is clear for me but b) is a guess (I checked some numbers)


The first and fastest counterexample is welcome (Or a proof ?)
First example: Taking n = 1, f = 1 divides 2p - 1 for any p.

First example with prime f: p = 3, n = 2; f = 2*22 - 1 = 7 divides 23 - 1 = 7.

Second example with prime f: p = 5, n = 4; f = 2*42 - 1 = 31 divides 25 - 1 = 31

48 other examples known where f = 2p - 1 is prime.

Hey, you didn't say f had to be a proper divisor -- or prime.

I checked the factor table of 2n - 1, odd n < 1200, and did not find any examples with f prime other than f = Mp

I didn't check for composite proper factors of the form 2*n2 - 1.

Last fiddled with by Dr Sardonicus on 2020-09-12 at 01:10 Reason: xingif posty
Dr Sardonicus is offline   Reply With Quote