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Partition of Integers with mod

  1. Dec 17, 2012 #1
    1. The problem statement, all variables and given/known data
    Are the following subsets partitions of the set of integers?

    The set of integers divisible by 4, the set of integers equivalent to 1 mod 4, 2 mod 4, and 3 mod 4.


    2. Relevant equations



    3. The attempt at a solution
    Yes, it is a partition of the set of integers. Consider 4/4 = 1, 5/4 = 1 R 1, 6/4 = 1 R 2, 7/4 = 1 R 3.

    However, how would you create a negative number like -5?
     
  2. jcsd
  3. Dec 17, 2012 #2

    Dick

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    I'm not too clear on what your argument is supposed to mean. What's R? But -5=3 mod 4 since (-5)=(-2)*4+3. Hmm, I think I see. R means 'remainder', yes?
     
    Last edited: Dec 17, 2012
  4. Dec 17, 2012 #3
    Sorry, I forgot to mention this is far from a formal proof. R just means remainder.
     
  5. Dec 17, 2012 #4

    Dick

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    Yeah, it is far from formal. But I see what you are doing. Are you supposed to give something formal or just answer yes or no?
     
  6. Dec 17, 2012 #5
    Just answer yes or no. And, you answered my question. I'm pretty sure the answer is yes. Thanks.
     
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