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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, Jun 30, 2014, 8:25 AM ![\[x^2+y^2=z^3+u^3\]](//latex.artofproblemsolving.com/a/6/0/a605aa157ecb8237281cb66c51192f6a313ae97b.png)
![\[x=q^6-2(a+s+t)q^5+(t^2-2(4a+3s)t-3a^2-10as-s^2)q^4-\]](//latex.artofproblemsolving.com/e/9/2/e92ae5edac8e91754b68772e46a865c9c257863a.png)
![\[-4(3t^3+(5a+4s)t^2+(3a^2+2as+s^2)t+a(a^2-s^2))q^3+\]](//latex.artofproblemsolving.com/e/8/a/e8a1fe5d84287b3be8c4d5fceb7a815e2394e44a.png)
![\[+(7t^4+4(a+s)t^3+6(3a^2+2as+s^2)t^2+4(3a^3+9sa^2+3as^2-s^3)t+3a^4+12sa^3+\]](//latex.artofproblemsolving.com/5/2/f/52fab4480113064fd559b65ebfb8579052c375a2.png)
![\[+18s^2a^2-4as^3-s^4)q^2-(t^2-2ts+a^2-2as-s^2)(10t^3+18(a+s)t^2+\]](//latex.artofproblemsolving.com/9/e/c/9ece625a265ef79afd0a6cf49af967f8aa1bf3bb.png)
![\[+2(5a^2+8as+5s^2)t+2(a^3+sa^2+as^2+s^3))q+(t^2-2at-a^2-2as+s^2)(7t^4+\]](//latex.artofproblemsolving.com/1/9/0/190375a973a6c44f4dd5b6e01a2999fddde8ccbc.png)
![\[+10(a+s)t^3+8(a^2+as+s^2)t^2+2(a^3+sa^2+as^2+s^3)t+a^4+2a^2s^2+s^4)\]](//latex.artofproblemsolving.com/5/c/3/5c31098b1fe1c77075e5ad5651912d512036cfc3.png)
![\[..............................................................\]](//latex.artofproblemsolving.com/6/6/0/6601487c96f6f66e00d92fc95d2e262ed8e61a00.png)
![\[y=q^6+2(a+s+t)q^5+(t^2-2(3a+4s)t-a^2-10as-3s^2)q^4+\]](//latex.artofproblemsolving.com/8/d/b/8dbf35266c8a3bf1447086e0e8c0acb093bb6622.png)
![\[+4(3t^3+(4a+5s)t^2+(a^2+2as+3s^2)t+s(s^2-a^2))q^3+\]](//latex.artofproblemsolving.com/b/f/3/bf3c33a10356815dec9b41ce316dddc52599811f.png)
![\[+(7t^4+4(a+s)t^3+6(a^2+2as+3s^2)t^2+4(-a^3+3sa^2+9as^2+3s^3)t-a^4-4sa^3+\]](//latex.artofproblemsolving.com/d/3/e/d3e370997b7269feb3e5ea451afa2688ac9315f0.png)
![\[+18a^2s^2+12as^3+3s^4)q^2+(t^2-2at-a^2-2as+s^2)(10t^3+18(a+s)t^2+\]](//latex.artofproblemsolving.com/2/4/c/24c02bfd7ea8699c3f22dc42f675ef8ee030498d.png)
![\[+2(5a^2+8as+5s^2)t+2(a^3+sa^2+as^2+s^3))q+(t^2-2ts+a^2-2as-s^2)(7t^4+\]](//latex.artofproblemsolving.com/2/b/b/2bb0ee73a4b743f7c207a3653d82d4c47866cdfc.png)
![\[.............................................................\]](//latex.artofproblemsolving.com/d/8/0/d802c737f53dd4e2849f4fb3f9ec73529d1526c3.png)
![\[z=q^4-2(t^2+a^2+s^2+4at+4as+4st)q^2-3t^4-8(a+s)t^3-\]](//latex.artofproblemsolving.com/9/5/0/95025137e3b5d6f78803b4b11faf528da4160cc4.png)
![\[-2(a^2+4as+s^2)t^2+a^4+2a^2s^2+s^4\]](//latex.artofproblemsolving.com/3/a/b/3ab145ee12277ad312a14a0fd2f754f29e43924c.png)
![\[u=(q^2+t^2+a^2+s^2)(q^2+5t^2+4(a+s)t+a^2+s^2)\]](//latex.artofproblemsolving.com/0/c/b/0cb477f73b56a6df72943d9a986bd1bfefbc2f4a.png)
- integers of any sign.![\[x^2+y^2=z^3+u^3\]](http://latex.artofproblemsolving.com/a/6/0/a605aa157ecb8237281cb66c51192f6a313ae97b.png)
![\[x=q^6-2(a+s+t)q^5+(t^2-2(4a+3s)t-3a^2-10as-s^2)q^4-\]](http://latex.artofproblemsolving.com/e/9/2/e92ae5edac8e91754b68772e46a865c9c257863a.png)
![\[-4(3t^3+(5a+4s)t^2+(3a^2+2as+s^2)t+a(a^2-s^2))q^3+\]](http://latex.artofproblemsolving.com/e/8/a/e8a1fe5d84287b3be8c4d5fceb7a815e2394e44a.png)
![\[+(7t^4+4(a+s)t^3+6(3a^2+2as+s^2)t^2+4(3a^3+9sa^2+3as^2-s^3)t+3a^4+12sa^3+\]](http://latex.artofproblemsolving.com/5/2/f/52fab4480113064fd559b65ebfb8579052c375a2.png)
![\[+18s^2a^2-4as^3-s^4)q^2-(t^2-2ts+a^2-2as-s^2)(10t^3+18(a+s)t^2+\]](http://latex.artofproblemsolving.com/9/e/c/9ece625a265ef79afd0a6cf49af967f8aa1bf3bb.png)
![\[+2(5a^2+8as+5s^2)t+2(a^3+sa^2+as^2+s^3))q+(t^2-2at-a^2-2as+s^2)(7t^4+\]](http://latex.artofproblemsolving.com/1/9/0/190375a973a6c44f4dd5b6e01a2999fddde8ccbc.png)
![\[+10(a+s)t^3+8(a^2+as+s^2)t^2+2(a^3+sa^2+as^2+s^3)t+a^4+2a^2s^2+s^4)\]](http://latex.artofproblemsolving.com/5/c/3/5c31098b1fe1c77075e5ad5651912d512036cfc3.png)
![\[..............................................................\]](http://latex.artofproblemsolving.com/6/6/0/6601487c96f6f66e00d92fc95d2e262ed8e61a00.png)
![\[y=q^6+2(a+s+t)q^5+(t^2-2(3a+4s)t-a^2-10as-3s^2)q^4+\]](http://latex.artofproblemsolving.com/8/d/b/8dbf35266c8a3bf1447086e0e8c0acb093bb6622.png)
![\[+4(3t^3+(4a+5s)t^2+(a^2+2as+3s^2)t+s(s^2-a^2))q^3+\]](http://latex.artofproblemsolving.com/b/f/3/bf3c33a10356815dec9b41ce316dddc52599811f.png)
![\[+(7t^4+4(a+s)t^3+6(a^2+2as+3s^2)t^2+4(-a^3+3sa^2+9as^2+3s^3)t-a^4-4sa^3+\]](http://latex.artofproblemsolving.com/d/3/e/d3e370997b7269feb3e5ea451afa2688ac9315f0.png)
![\[+18a^2s^2+12as^3+3s^4)q^2+(t^2-2at-a^2-2as+s^2)(10t^3+18(a+s)t^2+\]](http://latex.artofproblemsolving.com/2/4/c/24c02bfd7ea8699c3f22dc42f675ef8ee030498d.png)
![\[+2(5a^2+8as+5s^2)t+2(a^3+sa^2+as^2+s^3))q+(t^2-2ts+a^2-2as-s^2)(7t^4+\]](http://latex.artofproblemsolving.com/2/b/b/2bb0ee73a4b743f7c207a3653d82d4c47866cdfc.png)
![\[.............................................................\]](http://latex.artofproblemsolving.com/d/8/0/d802c737f53dd4e2849f4fb3f9ec73529d1526c3.png)
![\[z=q^4-2(t^2+a^2+s^2+4at+4as+4st)q^2-3t^4-8(a+s)t^3-\]](http://latex.artofproblemsolving.com/9/5/0/95025137e3b5d6f78803b4b11faf528da4160cc4.png)
![\[-2(a^2+4as+s^2)t^2+a^4+2a^2s^2+s^4\]](http://latex.artofproblemsolving.com/3/a/b/3ab145ee12277ad312a14a0fd2f754f29e43924c.png)
![\[u=(q^2+t^2+a^2+s^2)(q^2+5t^2+4(a+s)t+a^2+s^2)\]](http://latex.artofproblemsolving.com/0/c/b/0cb477f73b56a6df72943d9a986bd1bfefbc2f4a.png)
- integers of any sign.
December 2022
October 2022