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Perfect squares proof

  1. Feb 2, 2009 #1
    1. The problem statement, all variables and given/known data

    If C^2 = ab and the greatest common divisor of a and b is equal to 1, prove that a and b are perfect squares

    2. Relevant equations

    I know that if (a,b)=1, then there exists integers u and v where 1=au+bv (even though i don't think this is necessary in this proof)

    also, I know that the square root of a perfect square is a rational number, if it is not a perfect square, then it is irrational

    Lastly, I know that since (a,b)=1 that means a and b are relatively prime


    3. The attempt at a solution

    I have absolutely no idea how to do this proof. I know i need to show that the square root of a and the square root of b are rational, but I don't know how to do that.

    Maybe I could do it by trying to show it is irrational and finding a contradiction? Any help would be great!
     
  2. jcsd
  3. Feb 2, 2009 #2

    Dick

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    Homework Helper

    It's pretty easy conceptually if you think about the prime factorizations of a and b. Try that.
     
  4. Feb 3, 2009 #3
    Yeah, I figured it out like 10 minutes after i posted, it is really easy now that I thought of the prime factorizations of a and b. Thanks for the help though!
     
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