Results 1 to 3 of 3

Math Help - Divisor Questions

  1. #1
    Member
    Joined
    Nov 2008
    Posts
    152

    Divisor Questions

    1) Which positive integers have exactly four positive divisors?

    2) Let n be a positive integer. Show that \tau(2^n-1) \geq \tau(n)
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor undefined's Avatar
    Joined
    Mar 2010
    From
    Chicago
    Posts
    2,340
    Awards
    1
    Quote Originally Posted by Janu42 View Post
    1) Which positive integers have exactly four positive divisors?

    2) Let n be a positive integer. Show that \tau(2^n-1) \geq \tau(n)
    1) Integers of the form \,p_1p_2 or \,p^3.

    Because \tau(n) = \prod(\alpha_i+1) for n=p_1^{\alpha_1}\cdots.

    2) Haven't solved, except that it's obviously true for n prime.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Nov 2009
    Posts
    106
    For 2, note that if d\mid n then 2^d-1 \mid 2^n-1
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. b is a Zero Divisor ( I think)
    Posted in the Number Theory Forum
    Replies: 2
    Last Post: July 23rd 2011, 09:05 PM
  2. divisor
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: April 19th 2010, 06:33 AM
  3. sum of divisor
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: February 10th 2010, 03:02 PM
  4. divisor
    Posted in the Advanced Algebra Forum
    Replies: 5
    Last Post: April 17th 2009, 04:43 AM
  5. divisor
    Posted in the Discrete Math Forum
    Replies: 0
    Last Post: January 28th 2009, 05:57 AM

Search Tags


/mathhelpforum @mathhelpforum