Results 1 to 10 of 10
Like Tree1Thanks
  • 1 Post By Ant

Math Help - Modular Arithmetic help!

  1. #1
    Junior Member
    Joined
    Feb 2013
    From
    New York
    Posts
    28

    Modular Arithmetic help!

    so this is confusing, with mod arithmetic i see that you only need the remainder as an answer but i don't get how it is solved.

    like
    2 (equivalence sign) 4(mod 3)
    (3+4)(mod 5)
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Ant
    Ant is offline
    Member
    Joined
    Apr 2008
    Posts
    137
    Thanks
    4

    Re: Modular Arithmetic help!

    Quote Originally Posted by zhengcl86 View Post
    so this is confusing, with mod arithmetic i see that you only need the remainder as an answer but i don't get how it is solved.

    like
    2 (equivalence sign) 4(mod 3)
    (3+4)(mod 5)
    I don't understand your question, could you clarify?

    2 is not equal to 4 modulo 3. 4 is equal to 1 modulo 3.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Feb 2013
    From
    New York
    Posts
    28

    Re: Modular Arithmetic help!

    2 = 4(mod3) is a true/false question and the = sign after 2 is the one with the 3 bars the equivalence sign. since i don't know the code to put that in.

    like if i get something like (2-4)(mod 7) and (2+9)(mod 10) how would i go about solving those?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Ant
    Ant is offline
    Member
    Joined
    Apr 2008
    Posts
    137
    Thanks
    4

    Re: Modular Arithmetic help!

    Quote Originally Posted by zhengcl86 View Post
    2 = 4(mod3) is a true/false question and the = sign after 2 is the one with the 3 bars the equivalence sign. since i don't know the code to put that in.

    like if i get something like (2-4)(mod 7) and (2+9)(mod 10) how would i go about solving those?
    2 = 4 (mod 3) is false.

    Modulo arithmetic really isn't too bad once you get used to the idea. In fact, we often use modulo arithmetic to tell the time; For example, 13 o'clock = 1 o'clock. And, 20:00 = 8pm. This is all modulo 12.

    Two number are equal modulo n if they differ by a multiple of n.

    Perhaps the best way to write a number modulo n, is to write it as a number less than n but greater than 0.

    If you number is lager than n, subtract multiples of n until you reach a number less than n. If you have a negative number, add multiplies of n until you arrive at a number greater than 0 but less than n.

    so what is 4 modulo 3? Well, 4 -3 = 1. So 4 = 1 mod 3.

    What is -10 modulo 3? Keep adding multiples of 3 until you reach a number greater than 0 but less than 3. -10 = -7 = -4 = -1 = 2 mod (3)

    Addition and subtraction are easy, just work out the answer as usual, then add or subtract multiples of 3 until you arrive at a number greater than 0 but less than n.
    Thanks from zhengcl86
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Junior Member
    Joined
    Feb 2013
    From
    New York
    Posts
    28

    Re: Modular Arithmetic help!

    this kinda of helped a bit, even tho i have my phone's time set on 24 hour clock, but it wasn't clicking in my head. thank you
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Junior Member
    Joined
    Feb 2013
    From
    New York
    Posts
    28

    Re: Modular Arithmetic help!

    so how would congruence equations come into play?

    i have 2+n=3(mod7)

    so would the answer be n = 6 (mod 7) ??
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Ant
    Ant is offline
    Member
    Joined
    Apr 2008
    Posts
    137
    Thanks
    4

    Re: Modular Arithmetic help!

     2 + n = 3 \ (mod\7)

    Treat like a normal equation, and subtract 2 from both sides...

     n = 1 \ (mod\7)

    And you're done.

    Of course, this isn't the unique way of writing it, in fact:

     n = 1\ (mod\7) = 8\ (mod\ 7) = 15 \ (mod \7) = 22\ (mod\ 7) ...
    Follow Math Help Forum on Facebook and Google+

  8. #8
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,665
    Thanks
    1616
    Awards
    1

    Re: Modular Arithmetic help!

    Quote Originally Posted by zhengcl86 View Post
    so how would congruence equations come into play?
    i have 2+n=3(mod7)?
    I have different solution for you.

    If you can see that n=1 is clearly a solution here.

    Thus (\forall k\in\mathbb{Z})[1+7k] is also a solution.
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Junior Member
    Joined
    Feb 2013
    From
    New York
    Posts
    28

    Re: Modular Arithmetic help!

    hmm that seems understandable,
    and makes alot more sense now

    how about fractions? n/2 = 4(mod7)
    so n = 2(mod7)
    n=2(mod7) n=9(mod7) n=16(mod7) n=23(mod 7)
    would that be the solution?

    then it comes regular equations like
    3=(n-4)(mod7)
    so 3n-12(mod7)
    n=-3(mod7) n=5(mod7) n=12(mod7) n=19(mod7)

    is my math correct? lol thanks in advance!
    Follow Math Help Forum on Facebook and Google+

  10. #10
    Newbie
    Joined
    Mar 2013
    From
    Nederland
    Posts
    4

    Re: Modular Arithmetic help!

    For the first one, you get the idea, but you made a small mistake.

    If you have
     n/2 \equiv 4 (\mbox{mod } 7)
    then, as you would do usually, multiply (not divide!) both sides by 2, and you get
    n \equiv 8 (\mbox{mod } 7)
    Now, as Ant explained, this is not the only answer. In fact, the "best" or most "standard" answer is the one where n is equivalent to some number between 0 and 7; in this case, that would be  n \equiv 1 (\mbox{mod } 7).


    For the second equation, note that
     3 \equiv (n-4) (\mbox{mod } 7)
    is the same equation as
    n-4 \equiv 3 (\mbox{mod } 7).
    So, we again can just solve it like we would any regular equation, by adding 4 to both sides:
     7 \equiv n (\mbox{mod } 7)
    So our answer is n \equiv 7 (\mbox{mod } 7) (or better: n \equiv 0 (\mbox{mod } 7)).
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Modular arithmetic
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: December 13th 2012, 09:31 PM
  2. Modular arithmetic
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: November 10th 2012, 01:11 PM
  3. Modular Arithmetic
    Posted in the Number Theory Forum
    Replies: 3
    Last Post: March 24th 2011, 10:43 PM
  4. Modular arithmetic
    Posted in the Number Theory Forum
    Replies: 4
    Last Post: March 21st 2011, 03:40 AM
  5. Modular Arithmetic
    Posted in the Number Theory Forum
    Replies: 2
    Last Post: October 15th 2006, 07:07 PM

Search Tags


/mathhelpforum @mathhelpforum