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Homework Help: Help with proof using cases

  1. Mar 10, 2008 #1
    1. The problem statement, all variables and given/known data
    For each integer n, if n is odd then 8[tex]\left|[/tex] (n[tex]^{2}[/tex]-1)

    2. Relevant equations
    Def of an odd number 2q+1

    3. The attempt at a solution

    (2q+1)[tex]^{2}[/tex] -1
    4q[tex]^{2}[/tex] +4q+1-1
    4q[tex]^{2}[/tex] +4q
    Here is where I get stuck.... should I factor out the 4 and say that q[tex]^{2}[/tex] +q is an integer and therefore can be wrote as some integer r and therefore 8[tex]\left|[/tex] 4r?
  2. jcsd
  3. Mar 10, 2008 #2


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    Science Advisor
    Homework Helper

    Can you show q^2+q is divisible by 2 for any integer q? If so, then 4q^2+4q is divisible by 8.
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