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!

Prove that 4^(n+1) + 5 is divisible by 3

  1. Oct 13, 2008 #1
    Prove that 4^(n+1) + 5 is divisible by 3 for all non-negative integers n.

    Here's what I did:
    The Base Case, when n=0
    4^(0+1) + 5 = 4 + 5 = 9 --> divisible by 3

    Assume that 4^(k+1) + 5 is also divisible by 3 for all n=0,1,2,...k.
    Then it must also be true for k+1 and
    4^(k+1+1) + 5 = 4 x 4^(k+1) + 5

    My solution doesn't seem to be complete. Is there something wrong or missing?
     
  2. jcsd
  3. Oct 13, 2008 #2

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Re: Proofs

    Well, yes, it is surely not obvious, yet, that your last formula is divisible by 3: which is the whole point.

    How about writing 4 x 4^(k+1) as 3 x 4^(k+1)+ [4^(k+1)] so that 4 x 4^(k+1)+ 5 is equal to 3 x 4^(k+1)+ [4^(k+1)+ 5]? Can you see now that both terms are divisible by 3?
     
    Last edited: Oct 14, 2008
  4. Oct 13, 2008 #3
    Re: Proofs

    Thank you =) I see it now.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?