8/2 What does "x (mod y)" in mathematics mean?
\_ how are you a computer science undergraduate without knowing this?
it's the remainder of x divided by y.
\_ Use the distributive property:
x (mod y) = (x mod) (x y)
Makes sense now?
\_ I still don't get it. What does the latter mean?
\_ Man, I was kidding. Sorry about that. Seriously,
though, "mod" just means the remainder, like from
elementary school. So for example, 4 mod 3 is 1.
\_ You are missing the minor technical distinction between
"x mod y" and "... (mod y)", see below. -alexf
\_ Well there was no way for me to tell he was referring
to FLT until he brought it up. That would have changed
my explanation.
\_ But that's not the theorem. It shouldn't be
an = sign, but rather a "congruent" symbol,
which is 3 horizontal lines. It'd take a
little too much time to explain, so I'd
pick up a Math 55 text for more details.
\_ Well there was no way for me to tell he was
referring to FLT until he brought it up. That
would have changed my explanation.
\_ You're not being blamed; your explanation is
reasonable given that you weren't specifically
asked for distinction between mod and (mod).
-alexf
\_ I just read about the Fermat's Little Theorem, which
states "Let p be a prime which does not divide the
integer a, then a^(p-1) = 1 (mod p)". I don't understand
what the "1 (mod p)" part means. Isn't "1 (mod p)" always
1 for all p greater than 1?
\_ "(mod p)" after an _comparative statement_ means that
that statement is checked only after taking the
remainders of both sides when divided by p. So, the
following two lines, e.g., are equivalent:
a=b (mod p)
a mod p = b mod p
(Note that to make the different meaning of the "="
clear, the "proper" way to write the first line uses
a 3-line "=" sign instead of the usual =). -alexf |