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Prove that if a and b are both odd integer

  1. Sep 7, 2010 #1
    1. The problem statement, all variables and given/known data

    prove that if a and b are both odd integer, then [tex]16|(a^2+b^2-2)[/tex]

    2. Relevant equations


    3. The attempt at a solution

    let [tex]a=2m+1 \ and \ b=2n+1[/tex], then [tex]a^2+b^2-2=4(m(m+1)+n(n+1))[/tex] so its divisible by 4, and also divisible 8 since [tex]m(m+1) \ and \ n(n+1)[/tex] are even.
    so i only prove [tex]8|(a^2+b^2-2)[/tex], then how to continue? clue please T_T
  2. jcsd
  3. Sep 7, 2010 #2
    Re: divisibility

    hey i've got counter example, a=1 and b=3, so the question is wrong?
  4. Sep 7, 2010 #3
    Re: divisibility

    16\8=0 or am i wrong?
  5. Sep 7, 2010 #4
    Re: divisibility

    A thought..Let a^2 +b^2-2<> 16k. a^2+b^2<>16k+2 => a^2+b^2<>2m => odd +odd<> even which is wrong. (<> different from)
  6. Sep 7, 2010 #5


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    Science Advisor
    Homework Helper

    Re: divisibility

    3^2+7^2-2=56. That isn't divisible by 16 either. Yes, there is something wrong with the question.
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