Results 1 to 2 of 2

Math Help - prove this

  1. #1
    Member
    Joined
    Feb 2008
    Posts
    125

    prove this

    show that if a and n are positive integers with n>1, a>1 such that (a^n)+1 is prime, then n=2^k, where k is a positive integer.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    9
    Quote Originally Posted by mandy123 View Post
    show that if a and n are positive integers with n>1, a>1 such that (a^n)+1 is prime, then n=2^k, where k is a positive integer.
    If n is odd then x^n + y^n = (x+y)(x^{n-1}-x^{n-2}y+x^{n-3}y-...-xy^{n-2}+y^{n-2}).
    Thus, if n has a non-trivial odd factor p then a^n+1 = (a^m)^p + 1 = (a^m+1)(....) and it would not be prime.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Prove a/b and a/c then a/ (3b-7c)
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: March 23rd 2010, 05:20 PM
  2. prove,,,
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: March 1st 2010, 09:02 AM
  3. Prove |w + z| <= |w| +|z|
    Posted in the Algebra Forum
    Replies: 3
    Last Post: February 28th 2010, 05:44 AM
  4. Replies: 2
    Last Post: August 28th 2009, 02:59 AM
  5. How to prove that n^2 + n + 2 is even??
    Posted in the Algebra Forum
    Replies: 3
    Last Post: November 30th 2008, 01:24 PM

Search Tags


/mathhelpforum @mathhelpforum