Thanks all. I'm not officially releasing the ~ma until he starts, cause there was that one job where he lasted less than 6 hours...but still...this appears to be a good one.

Hil: why is a^p = a in Z sub p when p is prime? Also, if you divide f(x) by (x-a), why is the remainder always f(a)? It's sort of obvious why this is true for f(a)=0, but even when it isn't it's true, and I'm racking my brain as to why.

Steph, I don't know how much detail you need. There's lots of web sites, e.g. [link]

And of course I pretty much champ at the bit to explain anything mathy.

yay for mg's dh!

Deena - you hit it on the head. Oh boy did you!!!

I don't know what you mean by binary code.

I do know what you mean by binary code.

(No, I don't. I just wanted to go for the true binary X-post.)

Um. Maybe I'm referring to it incorrectly. But since I don't know anything about it, I don't know how I should be referring to it. So far the mathiest people in this thread don't know what I mean, and I don't know how to articulate what I mean.

If you were explaining the binary....system (? is that a better term?) to a retarded 3-year-old lemur, how would you explain it???

Or, what's the story with all the 0s and 1s? How does it work? How does one count with only 0s and 1s? How is that used in relation to computer programming? Or, *is* it used in relation to computer programming? How do a bunch of 0s and 1s make my iTunes work?

Steph, do you understand bases? Like the principle of base ten (decimal) vs. base eight?

Steph, do you understand bases? Like the principle of base 10 (decimal) vs. base 8?

Um. Someone explained base 8 recently -- I can't remember which thread -- and by "recently," I mean "in the past few or 6 months" -- and I sort of grasped the idea, but not really.

Base 10 is just....the numbering system that we common non-mathy folk use in everyday life, right? Because I get that. That's about the only math I get.

Binary is just counting when the largest digit you can use is 1.

So:

Regular Number   Binary Number
         0                     0
         1                     1
         2                    10
         3                    11
         4                   100
         5                   101
         6                   110
         etc...

why is a^p = a in Z sub p when p is prime?

That's a direct consequence of Fermat's Little Theorem. Have you learned that yet?

Also, if you divide f(x) by (x-a), why is the remainder always f(a)?

Hmm. I'm not sure about that one. You're assuming that f(x) is a polynomial? You can probably do something with the division algorithm, but I'm not sure exactly what.

Okay, but I don't understand that chart. How does 6 in normal numbers = 110 in binary?