Results 1 to 4 of 4

Math Help - Making numbers add up to square numbers

  1. #1
    Markdevs
    Guest

    Making numbers add up to square numbers

    Hi everyone,

    I'm stuck on this question and it's driving me crazy!!

    Basically you have to add numbers in a line of a triangle that will add up to a square number.

    e.g. a
    b c

    a&b have to add up to a square, as well as a&c and b&c.

    Any help would be appreciated.

    Can anyone help?
    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 Markdevs View Post
    Hi everyone,

    I'm stuck on this question and it's driving me crazy!!

    Basically you have to add numbers in a triangle that will add up to a square number.

    Can anyone help?
    you may want to be a little more specific than that
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    10,079
    Thanks
    375
    Awards
    1
    Quote Originally Posted by Markdevs View Post
    Hi everyone,

    I'm stuck on this question and it's driving me crazy!!

    Basically you have to add numbers in a line of a triangle that will add up to a square number.

    e.g. a
    b c

    a&b have to add up to a square, as well as a&c and b&c.

    Any help would be appreciated.

    Can anyone help?
    Do you mean like
    Code:
      -1
    2    2
    Or is there some restriction on the numbers a, b, c?

    -Dan
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    10,079
    Thanks
    375
    Awards
    1
    Quote Originally Posted by Markdevs View Post
    Hi everyone,

    I'm stuck on this question and it's driving me crazy!!

    Basically you have to add numbers in a line of a triangle that will add up to a square number.

    e.g. a
    b c

    a&b have to add up to a square, as well as a&c and b&c.

    Any help would be appreciated.

    Can anyone help?
    Code:
       a
    b    c
    such that
    a + b = x^2

    a + c = y^2

    b + c = z^2

    Subtracting the first two equations gives me
    a - c = x^2 - y^2

    Adding this equation to the third equation give me
    2b = x^2 - y^2 + z^2

    Thus
    b = \frac{x^2 - y^2 + z^2}{2}

    c = z^2 - \frac{x^2 - y^2 + z^2}{2} = \frac{-x^2 + y^2 + z^2}{2}

    a = x^2 - \frac{x^2 - y^2 + z^2}{2} = \frac{x^2 + y^2 - z^2}{2}

    You can pick any numbers x, y, z that you like.

    For example, letting x = 1, y = 2, and z = 3 gives
    Code:
       -2
     3    6
    -Dan

    EDIT: I can show that at least one of a, b, and c must be negative.
    Last edited by topsquark; November 18th 2007 at 09:28 AM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Why do we square numbers?
    Posted in the Math Topics Forum
    Replies: 5
    Last Post: August 3rd 2011, 04:56 AM
  2. square numbers
    Posted in the Number Theory Forum
    Replies: 8
    Last Post: May 4th 2010, 09:05 AM
  3. Square of 3 real numbers
    Posted in the Algebra Forum
    Replies: 2
    Last Post: April 27th 2010, 09:31 AM
  4. Square numbers
    Posted in the Algebra Forum
    Replies: 4
    Last Post: December 10th 2009, 09:52 AM
  5. square numbers
    Posted in the Algebra Forum
    Replies: 3
    Last Post: October 14th 2008, 08:13 PM

Search Tags


/mathhelpforum @mathhelpforum