theorem
working on some math stuff. in it i made use of a couple of reasonable assumptions, mainly:
for every integer k there is a fibonacci number that is a multiple of k.
for all integers a,b>0, if a and b are relatively prime, then there's an integer m>0 such that a^m = 1 (mod b).
first seems reasonable, right? I'm having the devil of a time proving it though; if you happen to know anything about this, please leave a comment? the second one seems weirder, but i've definitely seen it mentioned before, perhaps even with a famous name.
well now I'm trying to write down everything i have, all pretty like in LaTeX. as such, in addition to the embarrassing admission that I don't know anything about how to prove the first assumption, I had to try and track down the second one in formal form.
And lo and behold, after a bit of banging my head against the TCP/IP wall, Wikipedia finally delivered. In fact, after following its link about the totient function, (read: toilet function) it may end up answering a great deal more about what i'm writing about than I even thought possible at the moment. (In case you are reading and are interested, I will put a PDF up on this page later so you can know what i'm talking about.) It's a lot of information, though. A little bit intimidating and paralyzing
The one day Wikipedia turns out to be more useful to me than ever before, it's causing me information overload, which in some sense it also does when I'm wasting time.
for every integer k there is a fibonacci number that is a multiple of k.
for all integers a,b>0, if a and b are relatively prime, then there's an integer m>0 such that a^m = 1 (mod b).
first seems reasonable, right? I'm having the devil of a time proving it though; if you happen to know anything about this, please leave a comment? the second one seems weirder, but i've definitely seen it mentioned before, perhaps even with a famous name.
well now I'm trying to write down everything i have, all pretty like in LaTeX. as such, in addition to the embarrassing admission that I don't know anything about how to prove the first assumption, I had to try and track down the second one in formal form.
And lo and behold, after a bit of banging my head against the TCP/IP wall, Wikipedia finally delivered. In fact, after following its link about the totient function, (read: toilet function) it may end up answering a great deal more about what i'm writing about than I even thought possible at the moment. (In case you are reading and are interested, I will put a PDF up on this page later so you can know what i'm talking about.) It's a lot of information, though. A little bit intimidating and paralyzing
The one day Wikipedia turns out to be more useful to me than ever before, it's causing me information overload, which in some sense it also does when I'm wasting time.