For the system of equations:

by individ, Nov 18, 2014, 12:01 PM

For the system of equations:

\[\left\{\begin{aligned}&a^3+q^3+c^3=n^3+k^3+r^3\\&a+q-c=2(n+k-r)\end{aligned}\right.\]

Solutions have the form.

\[a=6(2x-2b+3y-z)(b^2+yz-yb-zb)\]

\[q=14b^3+z^3-7x^3-27y^3+12(z+2b-3y)x^2-\] \[-6(4b^2+9y^2+z^2-12by+4bz-6yz)x+\]
\[+3zb^2-45yb^2+57by^2+9bz^2-24yzb+24zy^2-12yz^2\]

\[c=2b^3+z^3-7x^3-27y^3+12(z+2b-3y)x^2-\] \[-6(4b^2+9y^2+z^2-12by+4bz-6yz)x+\]
\[+21zb^2-27yb^2+51by^2+3bz^2-48ybz+30zy^2-6yz^2\]

\[n=6x(b^2+yz-yb-zb)\]

\[k=8b^3+z^3-7x^3-27y^3+12(z+2b-3y)x^2-\] \[-6(4b^2+9y^2+z^2-12by+4bz-6yz)x+\]
\[+9zb^2-33yb^2+51by^2+9bz^2-36yzb+30zy^2-12yz^2\]

\[r=8b^3+z^3-7x^3-27y^3+12(z+2b-3y)x^2-\] \[-6(4b^2+9y^2+z^2-12by+4bz-6yz)x+\]
\[+15zb^2-39yb^2+57by^2+3bz^2-36yzb+24zy^2-6yz^2\]

$b,z,x,y$ - integers asked us.

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  • How did you discover these parametric solutions to diophantine equations?

    by fanzhuyifan, Dec 31, 2016, 9:25 AM

  • Russian? are you sure it ain't greek?

    by Mathisfun04, Dec 27, 2016, 4:03 PM

  • yep i agree

    by Eugenis, Oct 31, 2015, 2:40 AM

  • Best blog ever

    by FlakeLCR, Oct 13, 2015, 8:07 PM

  • too much russian.

    by rileywkong, Aug 21, 2015, 6:10 PM

  • Decided the equation.

    by individ, Aug 20, 2015, 5:05 AM

  • Some insight into how you figured it out?

    by Not_a_Username, Aug 19, 2015, 3:52 PM

  • I figured it out. Decided equation.

    by individ, Aug 19, 2015, 5:01 AM

  • Yes, how do you come up with the formula? :P

    by Not_a_Username, Aug 18, 2015, 10:29 PM

  • I don't understand. There are the equation and there is a formula to it solutions. What is the problem?

    by individ, Aug 13, 2015, 4:22 PM

  • What? Lol you are substituting solutions with literally no motivation

    by Not_a_Username, Aug 13, 2015, 12:59 PM

  • What replacement? Where?

    by individ, Aug 8, 2015, 5:37 AM

  • Darn, what are the motivation for these substitutions???

    by Not_a_Username, Aug 5, 2015, 10:44 AM

  • Are you greek?

    by beanielove2, Dec 24, 2014, 6:31 PM

  • So, a purely mathematical blog?

    by Lionfish, Dec 2, 2014, 1:20 PM

  • To prove that it is necessary to show the method of calculation. I do not want to do yet.

    by individ, Mar 28, 2014, 6:14 AM

  • I can't understand these posts....What language are they written in? I don't recognize it.

    I like your avatar! :P

    by 15cjames, Mar 11, 2014, 1:57 PM

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