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!

Proof involving divisibilty

  1. May 2, 2010 #1
    1. The problem statement, all variables and given/known data

    Show n4 - 1 is divisible by 5 when n is not divisible by 5.

    2. Relevant equations

    3. The attempt at a solution

    My thought here is proof by cases, one case being where n is divisible by 5 and the other case saying n is not divisible by 5. I am just not totally sure how to implement this strategy.
  2. jcsd
  3. May 2, 2010 #2
    If you split your second case a bit more that will do fine.
  4. May 3, 2010 #3


    User Avatar
    Science Advisor

    If n is not divisible by 5, then it is of the form n= 5k+ 1, n= 5k+ 2, n= 5k+ 3, or n= 5k+ 4.

    Or you can consider n= 5k- 2, n= 5k- 1, n= 5k+ 1, and n= 5k+ 2 if that makes the calculations simpler.
  5. May 4, 2010 #4
    If we would to spent a little more time to think through , we will realise that the determining factor will then lies in [tex]5k \pm m[/tex] such the [tex]m^{4}\equiv 1 (mod5)[/tex] with application with binomial theorem.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook