Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Problem with mod operation

  1. Sep 4, 2012 #1
    Hello
    i know that it shows Remaining for example

    5 mod 3=2
    1 mod 3=1

    but if i select negative number what does it do?

    example:

    -10 mod 27 =?

    Thanks
     
  2. jcsd
  3. Sep 4, 2012 #2
    In math, mod is defined as a relation, rather than an operator. So we would say

    5 [itex]\equiv[/itex] 2 (mod 3)

    and

    1 [itex]\equiv[/itex] 1 (mod 3)

    where the [itex]\equiv[/itex] in this context is pronounced "is congruent to."

    In other words a mod-n statement returns "true" or "false" when applied to pairs of numbers. The general rule is that

    a [itex]\equiv[/itex] b (mod n) if the number n divides a - b.

    Now a lot of people come to mod from programming languages, where mod is not a relation, but is rather an operator, meaning that it returns a single value. That's the usage you've written, so we say

    5 mod 3=2

    and so forth.

    But even though 5 [itex]\equiv[/itex] 2 (mod 3), it's also true that 5 [itex]\equiv[/itex] 47 (mod 3), right? Both 47 and 5 give the same remainder when divided by 3. [That's equivalent to the definition I gave earlier; but you should actually convince yourself of that]

    So if someone asks us what is 5 mod 3, what should the answer be? The convention is that we take the unique number x such that 5 [itex]\equiv[/itex] x (mod 3) and x is greater than or equal to 0, but less than 3.

    With that background, what is the answer to -10 mod 27 = ?

    Well, let's find x such that -10 [itex]\equiv[/itex] = x (mod 27), and x is between 0 and 26 inclusive. A moment's thought will convince you that x = 17 is the right answer here. So

    -10 mod 27 = 17

    That's because

    a) -10 - 17 is divisible by 27; and

    b) 17 is the unique number with that property that's also between 0 and 26, inclusive.

    That's a long answer but it's everything you need to know to make sense of this kind of problem.
     
    Last edited: Sep 4, 2012
  4. Sep 4, 2012 #3

    Bacle2

    User Avatar
    Science Advisor

    Maybe a quick way of answering is a=b mod c is equivalent to : c|(b-a) , or, the

    remainder of dividing a by c is b*. And complement it with Stevel27's answer.

    * This is a technical point, since we usually choose the remainder to be within

    a given range, but we can add multiples.
     
  5. Sep 4, 2012 #4
    Thanks Dear SteveL27 & Bacle2
    you are my best teacher that dedicate your time to telling me the right answer.

    Thanks again
     
  6. Sep 4, 2012 #5

    Bacle2

    User Avatar
    Science Advisor

    Thanks, but I did only a minimal part.

    That's how I like it, Stevel27 does 99%+ of the work and we split the credit in half ;) .
     
  7. Sep 4, 2012 #6
    I don't mind. I got 99% of the cash reward :-)
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook