Results 1 to 5 of 5
Like Tree3Thanks
  • 1 Post By SlipEternal
  • 1 Post By HallsofIvy
  • 1 Post By SlipEternal

Math Help - Showing a prime in an arithmetic progression

  1. #1
    Member
    Joined
    Oct 2012
    From
    san francisco
    Posts
    92

    Showing a prime in an arithmetic progression

    Hello I am stuck on this problem and I need some help on how to do this.

    Show that if p is a prime in the arithmetic progression 3n+1, n = 1,2,3,.... then it is also in the arithmetic progression 6n+1, n=1,2,3,.......
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Nov 2010
    Posts
    1,790
    Thanks
    693

    Re: Showing a prime in an arithmetic progression

    Start with an assumption. Assume that 3n+1 is prime. What do you know about all primes that are bigger than 3(1)+1?
    Thanks from gfbrd
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,368
    Thanks
    1313

    Re: Showing a prime in an arithmetic progression

    First, any number in the sequence 6n+ 1= 3(2n)+ 1 is also in the sequence 3n+1. To go the other way, from 3n+ 1 to 6m+ 1, we must have n= 2m, that is, n is even. 3n+ 1, with n odd, is even so every prime in the series 3n+1, which must be odd is of that form.
    Thanks from gfbrd
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Joined
    Nov 2010
    Posts
    1,790
    Thanks
    693

    Re: Showing a prime in an arithmetic progression

    Quote Originally Posted by HallsofIvy View Post
    First, any number in the sequence 6n+ 1= 3(2n)+ 1 is also in the sequence 3n+1. To go the other way, from 3n+ 1 to 6m+ 1, we must have n= 2m, that is, n is even. 3n+ 1, with n odd, is even so every prime in the series 3n+1, which must be odd is of that form.
    And that's what I was getting at with my question about primes bigger than 3(1)+1. They are all odd.
    Thanks from gfbrd
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Member
    Joined
    Oct 2012
    From
    san francisco
    Posts
    92

    Re: Showing a prime in an arithmetic progression

    Oh I see now thank you so much guys!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 9
    Last Post: August 9th 2012, 09:33 AM
  2. Arithmetic Progression
    Posted in the Pre-Calculus Forum
    Replies: 4
    Last Post: May 9th 2011, 02:36 AM
  3. Arithmetic Progression
    Posted in the Algebra Forum
    Replies: 3
    Last Post: January 12th 2011, 09:40 AM
  4. Arithmetic Progression or Arithmetic Series Problem
    Posted in the Math Topics Forum
    Replies: 1
    Last Post: October 8th 2009, 12:36 AM
  5. Replies: 8
    Last Post: March 23rd 2009, 07:26 AM

Search Tags


/mathhelpforum @mathhelpforum