Find Pythagorean number of a triangle

by daothanhoai, Oct 9, 2014, 10:42 AM

In proof 101th of Cut the Knot page, I found a form of Pythagorean theorem of any triangle. Now I proposed form of Pythagorean number of a triangle
Find all six positive interger numbers x,y,z,u,v,t such that:

$\left\{\begin{matrix} (x+y)^2=v(v+u)+z(z+t) & \\ (z+t)^2=u(u+v)+y(y+x)& \\ (u+v)^2=t(t+z)+x(x+y) &  \end{matrix}\right.$

See: http://www.cut-the-knot.org/pythagoras/index.shtml#101
This post has been edited 2 times. Last edited by daothanhoai, Oct 28, 2014, 1:01 PM

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Dao's blog back up: http://oaithanhdao.blogspot.com/

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daothanhoai
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  • hm i wonder who's 799786

    by heheman, May 12, 2025, 1:16 AM

  • Dead blog lmao

    by 799786, Jun 7, 2022, 11:30 PM

  • Nice Blog! :)

    by Functional_equation, Sep 6, 2020, 4:34 PM

  • Very useful blog :P

    by Kamran011, Apr 26, 2020, 11:26 AM

  • Dataaacvuuv

    by o_i-SNAKE-i_o, Dec 7, 2019, 8:58 AM

  • Wonderful work...so good to see!
    Can I ask you a question on the Simson live/Essay triangle?

    by Notacademic, Jul 13, 2019, 7:41 AM

  • Very Underrated....though amazing blog

    by AlastorMoody, Feb 23, 2019, 4:41 PM

  • Thank to You very much @utkarshgupta :P :P :P :P

    by daothanhoai, Jun 27, 2014, 11:18 AM

  • OK man !! :lol:
    This is some stuff !! :o

    Great Blog :D :D

    by utkarshgupta, Jun 22, 2014, 9:02 AM

  • :maybe: :maybe:

    by daothanhoai, Apr 13, 2014, 3:38 PM

  • I think no one here has a greater interest in Geometry than you have.

    by Ashutoshmaths, Mar 31, 2014, 1:12 PM

  • :maybe: :maybe: :o :P

    by daothanhoai, Feb 11, 2014, 7:06 AM

  • Thank to ThirdTimeLucky.

    by daothanhoai, Feb 11, 2014, 7:06 AM

  • Very nice problems, will surely try them after my exams! :) :oops:

    by ThirdTimeLucky, Feb 10, 2014, 9:02 PM

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