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Remainder of a number

  1. Aug 1, 2010 #1
    1. The problem statement, all variables and given/known data

    How much is the balance if u want to get integer value of ((2^1000) divided by 7))

    2. Relevant equations



    3. The attempt at a solution

    I need a little hint to start off with an attempt.
     
  2. jcsd
  3. Aug 1, 2010 #2

    HallsofIvy

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    Staff Emeritus
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    Since that is a rather large power of two, I suggest that you start with simple examples and see if you can find a pattern:

    [itex]2^0= 1[/itex]. Remainder on division by 7: 1
    [itex]2^1= 2[/itex]. Remainder on division by 7: 2
    [itex]2^2= 4[/itex]. Remainder on division by 7: 4
    [itex]2^3= 8[/itex]. Remainder on division by 7: 1
    [itex]2^4= 16[/itex]. Remainder on division by 7: 2
    [itex]2^5= 32[/itex]. Remainder on division by 7: 4
    [itex]2^6= 64[/itex]. Remainder on division by 7: 1
    [itex]2^7= 128[/itex]. Remainder on division by 7: 2
    [itex]2^8= 256[/itex]. Remainder on division by 7: 4

    Get the idea?
     
  4. Aug 1, 2010 #3
    Thanks Hallsofivy!
     
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