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Sum of two squares

  1. Jan 1, 2008 #1
    1. The problem statement, all variables and given/known data
    Prove that no prime three more than a multiple of four is a sum of two squares. (Hint: Work modulo 4.)


    2. Relevant equations



    3. The attempt at a solution

    a^2+b^2=4n+3=3 mod 4 is impossible if you look at the possibilities of a^2 and b^2.

    I did not use the fact that the number is prime. Am I missing something?
     
  2. jcsd
  3. Jan 1, 2008 #2

    Dick

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    Doesn't seem likely, does it?
     
  4. Jan 1, 2008 #3
    What doesn't seem likely?
     
  5. Jan 2, 2008 #4

    Dick

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    "Am I missing something?" doesn't seem likely. You checked squares are 0 or 1 mod 4. So the sum of two of them doesn't equal 3. Looks pretty bulletproof to me.
     
  6. Jan 2, 2008 #5

    Defennder

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    What does "prime three" here mean?
     
  7. Jan 2, 2008 #6

    HallsofIvy

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    It doesn't mean anything- but I did a double take myself when I read that. Perhaps commas would help: No prime, three more than a multiple of four, is a sum of two squares
     
  8. Jan 2, 2008 #7
    In my defense, Loren Larson (who is all-knowing) didn't think this sentence required any commas.
     
    Last edited: Jan 2, 2008
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