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