Results 1 to 6 of 6

Math Help - Sums of Squares problem.

  1. #1
    Junior Member
    Joined
    Apr 2008
    Posts
    26

    Sums of Squares problem.

    Let n = 17, 51, 37, 407, 629, 40885.

    (a) Decide whether n \in S_2.

    (b) If n \in S_2 find  a,b \in \mathbb{Z} with n=a^2+b^2.

    (c) If n \notin S_2 find  a,b,c,d \in \mathbb{Z} with  n=a^2+b^2+c^2+d^2.

    Thank you all for checking this out, and any ideas/suggestions are very welcome. Thanks!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    is up to his old tricks again! Jhevon's Avatar
    Joined
    Feb 2007
    From
    New York, USA
    Posts
    11,663
    Thanks
    3
    Quote Originally Posted by Proof_of_life View Post
    Let n = 17, 51, 37, 407, 629, 40885.

    (a) Decide whether n \in S_2.

    (b) If n \in S_2 find  a,b \in \mathbb{Z} with n=a^2+b^2.

    (c) If n \notin S_2 find  a,b,c,d \in \mathbb{Z} with  n=a^2+b^2+c^2+d^2.

    Thank you all for checking this out, and any ideas/suggestions are very welcome. Thanks!
    S_2 is the set of all numbers that are the sum of the squares of two integers?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Apr 2008
    Posts
    26
    S_2 is the set of all sums of 2 squares.

    Definition:
    For each integer k, greater than or equal to 1, let S_k = { n | n = (x_1)^2 + . . . + (x_k)^2 for some x_1 ,..., x_k \in \mathbb{Z} },the set of all sums of k squares.

    Sorry, and thanks!
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Opalg's Avatar
    Joined
    Aug 2007
    From
    Leeds, UK
    Posts
    4,041
    Thanks
    7
    Hint (just to get you started): a square has to be congruent to 0 or 1 mod 4.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Junior Member
    Joined
    Apr 2008
    Posts
    26
    So, let me say for the first one that n=17. Since 17 is congruent to 1 mod 4, that would satisfy part (a)? Since part (a) is satisfied, I would take part (b)'s approach and ignore part (c). The answer to part (b) would be  4^2 + 1^2 = 17 , where a=4 and b=1.

    I think I will get confused when n does not belong to  S_2 , and I will not know how to approach part (c).
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Junior Member
    Joined
    Apr 2008
    Posts
    26
    Sum of squares

    I should have just googled this earlier! Thanks to the last replier, it got me on the right track.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Fermat's theorem on sums of two squares
    Posted in the Number Theory Forum
    Replies: 3
    Last Post: August 2nd 2010, 12:33 PM
  2. Sums of squares
    Posted in the Number Theory Forum
    Replies: 13
    Last Post: January 7th 2010, 03:17 PM
  3. Sums of squares exercise
    Posted in the Number Theory Forum
    Replies: 2
    Last Post: December 19th 2009, 01:15 PM
  4. Sums of squares : putnam problem
    Posted in the Number Theory Forum
    Replies: 3
    Last Post: December 3rd 2009, 11:55 PM
  5. Sums of squares of positive integers prime to n
    Posted in the Number Theory Forum
    Replies: 1
    Last Post: November 23rd 2009, 11:15 PM

Search Tags


/mathhelpforum @mathhelpforum