Definition talk:Mersenne Number

I noticed that all Mersenne primes (apart from 3) seem to end in 1 or 7.

Anybody up for seeing whether, or showing how, all Mersenne numbers (apart from 3) end in 1 or 7? I've never seen anyone comment on it. It's probably really straightforward (and too obvious to be at all remarkable), I just haven't got to looking at it yet. Could it be as simple as that $2^n$ ends in $2$ or $8$ if $n$ is odd? Damme, of course it is. Silly bleedin' obvious question, forget I even posed it. --Matt Westwood 22:13, 7 April 2009 (UTC)

Actually, showing $x^n (mod 10)$ is periodic for all x might be interesting. --Cynic (talk) 00:48, 8 April 2009 (UTC)

Yes, I'm working on that one ... see the entry for Order of an Integer which is where I'll start from. --Matt Westwood 05:28, 8 April 2009 (UTC)