Results 1 to 2 of 2

Math Help - Square free problem

  1. #1
    Super Member
    Joined
    Mar 2006
    Posts
    705
    Thanks
    2

    Square free problem

    Prove that an integer n>1 is square-free iff n can be factored into a product of distinct primes.

    My proof.

    Assume n=p_{1}p_{2}...p_{n} for p being distinct primes. Since all the factors are no equal to one another, n cannot be divided by a square of an integer.

    conversely, assume n to be square free, then n cannot be divided by a square of an integer...
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    10
    Quote Originally Posted by tttcomrader View Post
    conversely, assume n to be square free, then n cannot be divided by a square of an integer...
    Correct. Because if n=p^2 p_1p_2... then p^2 divides n which makes it non-square free.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Square free numbers
    Posted in the Number Theory Forum
    Replies: 2
    Last Post: March 16th 2011, 09:47 PM
  2. Square free numbers
    Posted in the Number Theory Forum
    Replies: 3
    Last Post: June 14th 2009, 03:30 AM
  3. gaps between square free
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: September 23rd 2008, 07:19 PM
  4. square free
    Posted in the Number Theory Forum
    Replies: 0
    Last Post: July 12th 2008, 07:30 PM
  5. Square free problem 2
    Posted in the Number Theory Forum
    Replies: 3
    Last Post: January 31st 2008, 12:51 PM

Search Tags


/mathhelpforum @mathhelpforum