1. Not finding help here? Sign up for a free 30min 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!

Problem confirmation

  1. Mar 7, 2007 #1
    hi, i have nearly done this problem but made a mistake somewhere, hope you can help, thnx

    1. The problem statement, all variables and given/known data

    Prove that the difference between the equares of any two odd numbers is a multiple of 8.

    2. Relevant equations


    3. The attempt at a solution

    where r is an integer, and n is an integer:

    (2r-1)^2 - (2n-1)^2
    4r^2 - 4r + 1 - 4n^2 + 4n - 1
    4r^2 - 4r - 4n^2 + 4n
    4(r^2 - r - n^2 + n)

    now, that would show it to be multiple of 4, does this then suffice for proof for a multiple of 8? (8 a multiple of 4)

    thnx, just need a quick confirmation of this..

  2. jcsd
  3. Mar 7, 2007 #2


    User Avatar
    Science Advisor
    Gold Member

    You can reason this way:
    1) If both r and n are even, then each of r^2-n^2 and n-r must differ by a multiple of two, so their sum does too. The overall quantity is thus a multiple of eight.

    You can do the other two cases...
  4. Mar 7, 2007 #3


    User Avatar
    Science Advisor
    Homework Helper

    Or you can just show r^2-r is even for ANY r (so clearly so is n^2-n).
  5. Mar 8, 2007 #4
    soz, i dont mean to sound super noobish, but i dont quite understand how that works :S soz

    cna't someone please elabourate? thnx
  6. Mar 8, 2007 #5
    if r an n are both even , then r^2 and n^2 are even.
    that means r^2-n^2 is even, now since r and n are even then r-n is even.
    so (r^2 - r - n^2 + n) is even.
  7. Mar 8, 2007 #6
    o rite, i see that, but where does it go from there?
  8. Mar 8, 2007 #7
    "now, that would show it to be multiple of 4, does this then suffice for proof for a multiple of 8? (8 a multiple of 4)"

    Just for illustration purposes, 12 is a multiple of 4, because 4(3) = 12
    Does that mean 12 is a multiple of 8?
  9. Mar 9, 2007 #8
    o yeh, duh! stupid me, lol, i was getting in a muddle
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Problem confirmation