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Homework Help: Modulus operations

  1. May 30, 2007 #1
    1. The problem statement, all variables and given/known data
    How do you simplify : 1^3+2^3+3^3+4^3+.....+99^3+100^3(mod4)

    Please try to explain the solution as detailed as possible or atleast so I can understand it. :smile:
  2. jcsd
  3. May 30, 2007 #2

    D H

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    Use the fact that (4a+b)^3 mod 4 = b^3 mod 4. All you have to worry about are b=1,2,3,4. All of the other terms in the sum are duplicates.
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