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Homework Help: Basis arithmetic problem

  1. Jun 12, 2010 #1
    1. The problem statement, all variables and given/known data
    Hi everyone.
    I'm studying a problem and I need to prove that I have a basis. I tryed a proof and to achieve it I need to show that :

    if k divides a*b and also divides a2 +2*b2 Then k divides both a and b.


    2. Relevant equations

    I'm not sure what I'm asserting is true but if it was, then it would be great for me ( cause my proof would be finished).
    I first thought that if k divided a sum then it divided every term of that sum but I understood it was wrong (the other way is correct).

    I'm taking any idea!
     
  2. jcsd
  3. Jun 12, 2010 #2
    Re: Arithmetic-question

    No, what if a = b and k = a2 in general?
     
  4. Jun 12, 2010 #3
    Re: Arithmetic-question

    That's right indeed. But what if k is prime??
     
  5. Jun 12, 2010 #4
    Re: Arithmetic-question

    If k = 2, then no. Why? If k > 2 is prime, then yes. Why? Use the property that if p is prime and divides ab, then it divides a or b.
     
  6. Jun 13, 2010 #5
    Re: Arithmetic-question

    I can see if k>2, thank you, but why is it wrong if k=2 ?
     
  7. Jun 13, 2010 #6
    Re: Arithmetic-question

    Let a be even and b be odd.
     
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