Cube with 6 cubes.

by individ, Dec 25, 2015, 9:39 AM

For the equation.

$$x_1^3+x_2^3+x_3^3+x_4^3+x_5^3+x_6^3=x_7^3$$
You can write a fairly simple formula.

$$x_1=t^2-3(k+s)(p+t)+3p^2+6k^2+6s^2$$
$$x_2=2t^2+3((k+s)(p-t)-2pt)+6p^2+3k^2+3s^2$$
$$x_3=t^2-3(p+s)(k+t)+3k^2+6p^2+6s^2$$
$$x_4=2t^2+3((p+s)(k-t)-2kt)+6k^2+3p^2+3s^2$$
$$x_5=t^2-3(p+k)(s+t)+3s^2+6p^2+6k^2$$
$$x_6=2t^2+3((p+k)(s-t)-2st)+6s^2+3p^2+3k^2$$
$$x_7=3(t^2-2(p+k+s)t+3(p^2+k^2+s^2))$$
number theory
Diophantine equation

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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

17 shouts
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Diophantine equation
number theory
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