Hint for problem 1

: 136.376 Intro to Analysis: Hint for problem 1
   By Adam Majer on Thursday, September 06, 2001 - 06:43 pm: Edit Post

Hi all, [whoever is listening :-]

i mod j means the good old remainder for i/j

Hope this clears things up,
Adam


   By Anonymous on Friday, September 07, 2001 - 09:33 am: Edit Post

So, does x=y(mod6) mean the remainder of x/y is 6 ?


   By Robert Young on Friday, September 07, 2001 - 09:39 pm: Edit Post

Not quite. These are called congruences.

Basically,

a º b (mod n) means "a equals b modulo n" or, I guess, "a and b have the same remainder when divided by n"

You can do some neat things, like add, subtract and multiply from both sides and keep equality (division is another story). There is a lot more stuff, but i don't remember it all off hand. This is the first page to come from google when you search for "congruences".

When I took 74.213 (Discrete Math for Computer Scientists) I took congruences, and it makes proofs like "If x-y is even, then x2-y2 is divisible by 4", "Every cube is of the form 9n, 9n+1, or 9n-1" and other divisibility problems a fair bit easier, at least computation-wise.


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