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Mathematical Proof

  1. Feb 8, 2005 #1
    I'm given the statement: if m^2 is of the form 4k+3, then m is of the form 4k+3. I don't even know how to begin proving this. I'm guessing by contraposition.
     
  2. jcsd
  3. Feb 8, 2005 #2
    You put this already under general math
     
  4. Feb 8, 2005 #3

    mathwonk

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    good guess. if m is not of form 4k+3 thern m is of form 4k, 4k+1, or 4k+2. see what that gives.
     
  5. Feb 8, 2005 #4
    Please explain what you mean.
     
  6. Feb 8, 2005 #5

    mathwonk

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    all integers m are of one of the three forms 4k, 4k+1, 4k+2, or 4k+3, since when you divide an integer by 4, you get a remainder which is either 0,1,2, or 3.
     
  7. Feb 8, 2005 #6
    The only way that m^2 = 4k+3 AND m = 4k+3 is if m=1

    Is this what you meant?
     
  8. Feb 9, 2005 #7
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