Results 1 to 11 of 11

Math Help - Perfect Number!!! Help

  1. #1
    Junior Member
    Joined
    Nov 2009
    Posts
    33

    Perfect Number!!! Help

    An integer n is called a perfect number if it equals the sum of all of its positive divisors (excluding itself). For example, 28 is perfect as the divisors of 28 are 1, 2, 4, 7, 14 and 28, and 1 + 2 + 4 + 7 + 14 = 28. Show that if (2^p) − 1 is a prime number, then (2^(p−1))*((2^p) − 1) is a perfect number.

    can any one help me?
    really stuck
    not stuck no idea where to start
    Last edited by AwesomeDesiKid; November 16th 2009 at 08:25 AM. Reason: correct
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Apr 2009
    Posts
    678
    Thanks
    1
    Quote Originally Posted by AwesomeDesiKid View Post
    An integer n is called a perfect number if it equals the sum of all of its positive divisors (excluding itself). For example, 28 is perfect as the divisors of 28 are 1, 2, 4, 7, 14 and 28, and 1 + 2 + 4 + 7 + 14 = 28. Show that if (2^p) − 1 is a prime number, then (2^(p−1))*((2^p) − 1) is a perfect number.

    can any one help me?
    really stuck
    not stuck no idea where to start
    Hint: What are the factors of p^2, where p is a prime?
    So, in your question what are the factors of (2^(p−1))*((2^p) − 1)?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Nov 2009
    Posts
    33
    Quote Originally Posted by aman_cc View Post
    Hint: What are the factors of p^2, where p is a prime?
    So, in your question what are the factors of (2^(p−1))*((2^p) − 1)?
    i don't see it
    can you explain?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member
    Joined
    Apr 2009
    Posts
    678
    Thanks
    1
    Quote Originally Posted by AwesomeDesiKid View Post
    i don't see it
    can you explain?
    From the prime factorization get all the factors of the number. Things will look easy from there.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Member
    Joined
    Oct 2009
    Posts
    95
    Stronger hint:

    \underbrace{2^0}  \cdot \underbrace{ 2^{p-1} \cdot \left(2^p-1 \right)} =\underbrace{ 2^1} \cdot \underbrace{ 2^{p-2} \cdot \left(2^p-1 \right)}= ...
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Junior Member
    Joined
    Nov 2009
    Posts
    33
    Quote Originally Posted by gmatt View Post
    Stronger hint:

    \underbrace{2^0}  \cdot \underbrace{ 2^{p-1} \cdot \left(2^p-1 \right)} =\underbrace{ 2^1} \cdot \underbrace{ 2^{p-2} \cdot \left(2^p-1 \right)}= ...
    thanks guys
    but i got up to there actually
    but thats where im stuckkk
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Member
    Joined
    Oct 2009
    Posts
    95
    Sum up all the factors that you found and prove that they are equal to the original number.
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Junior Member
    Joined
    Nov 2009
    Posts
    33
    Quote Originally Posted by gmatt View Post
    Sum up all the factors that you found and prove that they are equal to the original number.
    i think i m messing up my summation
    cause its not adding up rite
    Follow Math Help Forum on Facebook and Google+

  9. #9
    Member
    Joined
    Oct 2009
    Posts
    95
    show your work so far.
    Follow Math Help Forum on Facebook and Google+

  10. #10
    Junior Member
    Joined
    Nov 2009
    Posts
    33
    Quote Originally Posted by gmatt View Post
    show your work so far.
    how don't know how to insert my math in to formula thing like you did
    and my sum is going for ever
    Follow Math Help Forum on Facebook and Google+

  11. #11
    Member
    Joined
    Oct 2009
    Posts
    95
    Just write your math as best yuo can, to insert math like I do you have to use the [HTML][/HTML] tags and use latex code.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Perfect number
    Posted in the Discrete Math Forum
    Replies: 3
    Last Post: May 30th 2011, 08:58 AM
  2. Perfect Number Proof
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: November 18th 2009, 12:22 AM
  3. Odd perfect number
    Posted in the Number Theory Forum
    Replies: 0
    Last Post: June 13th 2009, 08:58 PM
  4. Perfect Number
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: February 15th 2009, 08:08 PM
  5. Divisor of perfect number is not perfect
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: March 18th 2008, 02:26 PM

Search Tags


/mathhelpforum @mathhelpforum