Results 1 to 3 of 3

Thread: Square free numbers

  1. #1
    Member
    Joined
    Nov 2010
    Posts
    95

    Representing as sum of two squares

    Hi, how can one find the number of ways in which an integer can be expressed as a sum of two squares?
    E.g for 5 it's 1, as 5 can be represented as : 1^2+2^2.
    Here a^a+b^b is same as b^b+a^a.
    I know that for an integer to be expressed as such , its prime factorisation should contain no odd powers of primes of the form 4k + 3 . So how do i extend this idea to arrive at the conclusion or is there any other way/formula?
    Thanks.
    Last edited by pranay; Mar 12th 2011 at 04:17 AM. Reason: sorry, wrong title
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Opalg's Avatar
    Joined
    Aug 2007
    From
    Leeds, UK
    Posts
    4,041
    Thanks
    10
    Quote Originally Posted by pranay View Post
    Hi, how can one find the number of ways in which an integer can be expressed as a sum of two squares?
    E.g for 5 it's 1, as 5 can be represented as : 1^2+2^2.
    Here a^a+b^b is same as b^b+a^a.
    I know that for an integer to be expressed as such , its prime factorisation should contain no odd powers of primes of the form 4k + 3 . So how do i extend this idea to arrive at the conclusion or is there any other way/formula?
    See here for a relevant discussion.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    Nov 2010
    Posts
    95
    Thank.
    I worked out the problem, as:
    factorise the number and count the number of factors which are such that factor%4=3 (call these types d1) and factor%4=1 (call these types as d2).
    Then the number of ways of representing the number would be |d1-d3|/2 .
    Now this may take some time for factoring large numbers.So is there any other method to get d1(i.e no of factors with property : factor%4=1) and d3(i.e no of factors with property : factor%4=3) for a number?
    Thanks .
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. a question on square-free numbers
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: Apr 28th 2010, 09:45 PM
  2. Square free numbers
    Posted in the Number Theory Forum
    Replies: 3
    Last Post: Jun 14th 2009, 02:30 AM
  3. gaps between square free
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: Sep 23rd 2008, 06:19 PM
  4. square free
    Posted in the Number Theory Forum
    Replies: 0
    Last Post: Jul 12th 2008, 06:30 PM
  5. Square free problem 2
    Posted in the Number Theory Forum
    Replies: 3
    Last Post: Jan 31st 2008, 11:51 AM

Search Tags


/mathhelpforum @mathhelpforum