1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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


    User Avatar
    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.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook