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How did you discover these parametric solutions to diophantine equations?
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fanzhuyifan, Dec 31, 2016, 9:25 AM
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Russian? are you sure it ain't greek?
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Mathisfun04, Dec 27, 2016, 4:03 PM
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yep i agree
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Eugenis, Oct 31, 2015, 2:40 AM
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Best blog ever
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FlakeLCR, Oct 13, 2015, 8:07 PM
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too much russian.
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rileywkong, Aug 21, 2015, 6:10 PM
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Decided the equation.
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individ, Aug 20, 2015, 5:05 AM
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Some insight into how you figured it out?
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Not_a_Username, Aug 19, 2015, 3:52 PM
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I figured it out. Decided equation.
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individ, Aug 19, 2015, 5:01 AM
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Yes, how do you come up with the formula?
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Not_a_Username, Aug 18, 2015, 10:29 PM
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I don't understand. There are the equation and there is a formula to it solutions. What is the problem?
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individ, Aug 13, 2015, 4:22 PM
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What? Lol you are substituting solutions with literally no motivation
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Not_a_Username, Aug 13, 2015, 12:59 PM
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What replacement? Where?
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individ, Aug 8, 2015, 5:37 AM
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Darn, what are the motivation for these substitutions???
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Not_a_Username, Aug 5, 2015, 10:44 AM
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Are you greek?
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beanielove2, Dec 24, 2014, 6:31 PM
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So, a purely mathematical blog?
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Lionfish, Dec 2, 2014, 1:20 PM
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To prove that it is necessary to show the method of calculation. I do not want to do yet.
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individ, Mar 28, 2014, 6:14 AM
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I can't understand these posts....What language are they written in? I don't recognize it.
I like your avatar!
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15cjames, Mar 11, 2014, 1:57 PM
by individ, Aug 15, 2014, 9:29 AM ![\[\left\{\begin{aligned}& xy+xt=z^2\\&xy+yt=q^2\end{aligned}\right.\]](//latex.artofproblemsolving.com/1/e/e/1ee8d4cc4923c1580425c56498347a9ddf4de8b5.png)
![\[x=5p^2+30ps+45s^2\]](//latex.artofproblemsolving.com/d/a/4/da4cc7d119c8e0b0c8ad6a0ca12115c2209ec920.png)
![\[y=p^2+10ps+25s^2\]](//latex.artofproblemsolving.com/9/3/d/93d38d629739d4baa4c23e02522e2f223649d5e0.png)
![\[t=4p^2+30ps+55s^2\]](//latex.artofproblemsolving.com/7/c/7/7c740c000328dc8589da77c0054d9e263a12daa0.png)
![\[z=5p^2+35ps+60s^2\]](//latex.artofproblemsolving.com/3/e/6/3e6677452d64f359dcce0f384d717d999a8f601f.png)
![\[q=3p^2+25ps+50s^2\]](//latex.artofproblemsolving.com/b/c/6/bc6a335bdf85a4727925d0ac2150b7d3554da533.png)
![\[...\]](//latex.artofproblemsolving.com/a/7/7/a77a80061f2acc5bff28985d471dadc862f24425.png)
![\[x=5s^2\]](//latex.artofproblemsolving.com/4/a/6/4a61a80d60495f405decbf654024398f4382554a.png)
![\[y=4p^2+20ps+25s^2\]](//latex.artofproblemsolving.com/4/9/9/499c95cd2ffcee77abee290a6c53d6de7fc7a149.png)
![\[t=p^2-5s^2\]](//latex.artofproblemsolving.com/b/c/3/bc3eff91d0b032984d515e710b80fd6bd8834f2e.png)
![\[z=5ps+10s^2\]](//latex.artofproblemsolving.com/6/6/b/66b9f320de2c935710e791a379c66ded07654ab8.png)
![\[q=2p^2+5ps\]](//latex.artofproblemsolving.com/a/a/8/aa8c5e17a1a189c953a77a7b953e99becd43de1f.png)
For this we need to solve the Pell equation: 
![\[\left\{\begin{aligned}& xy+xt=z^2\\&xy+yt=q^2\end{aligned}\right.\]](http://latex.artofproblemsolving.com/1/e/e/1ee8d4cc4923c1580425c56498347a9ddf4de8b5.png)
![\[x=5p^2+30ps+45s^2\]](http://latex.artofproblemsolving.com/d/a/4/da4cc7d119c8e0b0c8ad6a0ca12115c2209ec920.png)
![\[y=p^2+10ps+25s^2\]](http://latex.artofproblemsolving.com/9/3/d/93d38d629739d4baa4c23e02522e2f223649d5e0.png)
![\[t=4p^2+30ps+55s^2\]](http://latex.artofproblemsolving.com/7/c/7/7c740c000328dc8589da77c0054d9e263a12daa0.png)
![\[z=5p^2+35ps+60s^2\]](http://latex.artofproblemsolving.com/3/e/6/3e6677452d64f359dcce0f384d717d999a8f601f.png)
![\[q=3p^2+25ps+50s^2\]](http://latex.artofproblemsolving.com/b/c/6/bc6a335bdf85a4727925d0ac2150b7d3554da533.png)
![\[...\]](http://latex.artofproblemsolving.com/a/7/7/a77a80061f2acc5bff28985d471dadc862f24425.png)
![\[x=5s^2\]](http://latex.artofproblemsolving.com/4/a/6/4a61a80d60495f405decbf654024398f4382554a.png)
![\[y=4p^2+20ps+25s^2\]](http://latex.artofproblemsolving.com/4/9/9/499c95cd2ffcee77abee290a6c53d6de7fc7a149.png)
![\[t=p^2-5s^2\]](http://latex.artofproblemsolving.com/b/c/3/bc3eff91d0b032984d515e710b80fd6bd8834f2e.png)
![\[z=5ps+10s^2\]](http://latex.artofproblemsolving.com/6/6/b/66b9f320de2c935710e791a379c66ded07654ab8.png)
![\[q=2p^2+5ps\]](http://latex.artofproblemsolving.com/a/a/8/aa8c5e17a1a189c953a77a7b953e99becd43de1f.png)
For this we need to solve the Pell equation: 
December 2022
October 2022