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Factorization of rings problem

  1. May 30, 2009 #1
    1. The problem statement, all variables and given/known data

    in order to factorize 20 on the rings of [tex] Q( \sqrt 2) [/tex] i must solve

    2. Relevant equations

    [tex] x^{2} -2y^{2}=10 [/tex]

    3. The attempt at a solution

    i do not know how to solve it, i have tried by brute force with calculator but can not get any response , the given hint is that [tex] x^{2} -2y^{2}=5 [/tex] has no solution.
     
  2. jcsd
  3. May 30, 2009 #2

    matt grime

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    Re: factorization

    I can only guess that you've factored 20 as 2*10, so why have you not factored 10 as 2*5?
     
  4. May 30, 2009 #3
    Re: factorization

    according to the teacher, who put the exercise the diophantine equation

    [tex] x^{2}-2y^{2}=5 [/tex] has no solution on integers.
     
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