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!

Algebra: show that x > 1 is prime

  1. Nov 16, 2009 #1
    1. The problem statement, all variables and given/known data
    2.4 Show that x > 1 is prime, iff x doesn't have any divisor t; where 1 < t [tex]\leq \sqrt{x}[/tex]. It is given that x,t [tex]\in[/tex] N.

    2. Relevant equations
    ?

    3. The attempt at a solution
    The "iff" thing makes me think; what can I do to show this?
    I have to show that x (x can be 2, 3, 4, 5, 6, ...) is prime if there is no "t", 1<t[tex]\leq \sqrt{x}[/tex] (t can be 1, 2, 3, 4, ...) that divides x. AND that that there is no t that divides x if x is prime.
    So I have to show it 2 ways.
    First: x is prime if t doesn't divide x
    Second: t doesn't divide x if x is prime

    And well, that's all I got! Please help.
    Vince, fresmen physics.
     
  2. jcsd
  3. Nov 16, 2009 #2

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    Welcome to PF!

    Hi Vince! Welcome to PF! :smile:

    (have a square-root: √ and a ≤ :wink:)

    Try starting with the opposite

    suppose x is not prime, and all its factors (two or more) are > √x. :wink:
     
  4. Nov 21, 2009 #3
    Re: Welcome to PF!

    Thanks for the welcome tim!
    Okay, so you said: suppose x is not prime, and all its factors are > √x

    I really have no idea what I can do with that...I tried, for a few days, but I just don't get it!
    Maybe you can explain it a bit more?
    Tnx!
     
  5. Nov 21, 2009 #4

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    Hi Vince00! :smile:

    Take 103 and 105 …

    how many factors can they have > 10 ? :wink:
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Algebra: show that x > 1 is prime
  1. Primes of the form 4n+1 (Replies: 10)

  2. Show that if x a (Replies: 5)

Loading...