Results 1 to 5 of 5

Math Help - proving the converse theorem

  1. #1
    Member
    Joined
    Nov 2006
    Posts
    123

    Question proving the converse theorem

    Here is another question that I got stuck with. Please see attachment. I typed the question in " Microsoft word" . If you can't load the attachment , please do let me know.

    Thank you very much.
    Attached Files Attached Files
    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 Jenny20 View Post
    Here is another question that I got stuck with. Please see attachment. I typed the question in " Microsoft word" . If you can't load the attachment , please do let me know.

    Thank you very much.
    Did you consider using the Mobius inversion formula?

    If g(n)=\sum_{d|n} f(d)is multiplicative then,

    f(n)=\sum_{d|n} \mu (n/d) \cdot g(d)

    Now, g(n) is multiplicative function
    And \mu(n) (the Mobius mu function) is also multiplicative.
    Thus,
    g(n)\cdot \mu(n) is also multiplicative.
    Thus,
    f(n) is multiplicative (because of the summation theorem).
    Last edited by ThePerfectHacker; December 27th 2006 at 01:22 PM.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Nov 2006
    Posts
    123
    Hi perfecthacker,

    Thank you very much for your reply. I have never learnt Mobius inversion forumla. I will go through your prove. If I don't understand it, I will come back to you.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Member
    Joined
    Nov 2006
    Posts
    123
    Hi perfecthacker,

    Can you show me the other way ( not by mobius inversion forumla) to prove this question? I don't really get your prove because I dont' quite understand the mobius inversion formula. Thank you very much for your help.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    10
    Quote Originally Posted by Jenny20 View Post
    Hi perfecthacker,

    Can you show me the other way ( not by mobius inversion forumla) to prove this question? I don't really get your prove because I dont' quite understand the mobius inversion formula. Thank you very much for your help.
    I just looked up the proof in my number theory book and they prove it the same way I did. Thus, perhaps this is the standard way.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Pythagorean Theorem and Converse
    Posted in the Geometry Forum
    Replies: 3
    Last Post: January 29th 2011, 07:48 PM
  2. [SOLVED] Help proving by Mean value theorem
    Posted in the Calculus Forum
    Replies: 3
    Last Post: November 17th 2010, 07:24 PM
  3. converse to thales theorem
    Posted in the Geometry Forum
    Replies: 1
    Last Post: September 15th 2010, 04:07 PM
  4. Replies: 0
    Last Post: November 13th 2009, 06:41 AM
  5. Converse of Fermat's Little Theorem (particular case)
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: April 30th 2009, 01:02 PM

Search Tags


/mathhelpforum @mathhelpforum