Results 1 to 2 of 2

Math Help - Proof with prime numbers

  1. #1
    Newbie
    Joined
    Oct 2009
    Posts
    24

    Proof with prime numbers

    Given that p doesn't divide n for all primes p is less than equal to the cube root of n, show that n> is either a prime or the product of two primes.

    I was given a hint and I was told to assume to the contrary that n contains at least 3 prime factors.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    May 2008
    Posts
    2,295
    Thanks
    7
    Quote Originally Posted by MichaelG View Post
    Given that p doesn't divide n for all primes p is less than equal to the cube root of n, show that n> is either a prime or the product of two primes.

    I was given a hint and I was told to assume to the contrary that n contains at least 3 prime factors.
    suppose n=\prod_{i=1}^k p_i, where k \geq 3 and p_1 \leq p_2 \leq \cdots \leq p_k are primes. then p_1^3 \leq p_1^k \leq \prod_{i=1}^k p_i = n. contradiction!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Cyclic group, relatively prime numbers proof
    Posted in the Algebra Forum
    Replies: 1
    Last Post: October 11th 2011, 08:45 PM
  2. Proof that all numbers>1 are divisable by a prime.
    Posted in the Number Theory Forum
    Replies: 7
    Last Post: July 13th 2011, 12:33 PM
  3. Proof involving prime numbers
    Posted in the Number Theory Forum
    Replies: 4
    Last Post: March 7th 2011, 02:38 PM
  4. proof with perfect and prime numbers
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: September 28th 2010, 07:46 PM
  5. Proof relating to prime numbers
    Posted in the Number Theory Forum
    Replies: 6
    Last Post: January 13th 2010, 11:31 AM

Search Tags


/mathhelpforum @mathhelpforum