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!

Beginner proof problem

  1. Jan 15, 2014 #1
    1. The problem statement, all variables and given/known data

    I'm given this problem and I think I'm supposed to use the same or similar method to solve both of its parts:

    a) Factor [tex] 2^{15} - 1 = 32,767 [/tex] into a product of two smaller positive integers.
    b) Find an integer [tex] x [/tex] such that [tex] 1 < x < 2^{32767} - 1 [/tex] and [tex] 2^{32767} [/tex] is divisible by [tex] x [/tex].
    2. Relevant equations

    It is shown above the problem that:
    [tex] x = 1 * 2 * 3 * 4 * ... * (n + 1) + 2 = 2 * (1 * 3 * 4 * ... *(n + 1) + 1 [/tex]
    While I get that it's true, I don't quite see how I can apply the same to solving the problem.Can anyone give a hint?

    3. The attempt at a solution

    I tried "guessing", however with no success.
     
    Last edited: Jan 15, 2014
  2. jcsd
  3. Jan 15, 2014 #2

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    I don't see any connection between the two.
    Can you factorise x3-1?
     
  4. Jan 16, 2014 #3

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    For b, you realize that [itex]2^{32767}[/itex] can be divided evenly only by another power of 2, right? So x must be a power of 2.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Beginner proof problem
Loading...