Timeline for Quadratic Diophantine equation in $\mathbb Z[T]$
Current License: CC BY-SA 3.0
13 events
| when toggle format | what | by | license | comment | |
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| Sep 16, 2015 at 21:26 | comment | added | Yemon Choi | Downvoting because the question asks for all solutions, and individ does not give any justification for his or her claim that this method produces all the solutions. | |
| S Aug 29, 2015 at 4:15 | history | suggested | joaopa | CC BY-SA 3.0 |
Some families of solutions
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| Aug 29, 2015 at 3:57 | vote | accept | joaopa | ||
| Aug 29, 2015 at 3:56 | review | Suggested edits | |||
| S Aug 29, 2015 at 4:15 | |||||
| Aug 21, 2015 at 6:45 | comment | added | joaopa | I checked your two solutions solution Both are correct. But you did not give any proof that there does not exist other solutions. Mathematics is not a matter of trust but proofs | |
| Aug 21, 2015 at 4:57 | comment | added | individ | @joaopa If Maple does not agree, then this problem Maple, not mine. Carefully substitute and check. You should have in the first formula. $$x=3(73-8T-12T^2)$$ $$y=4(3T+2)$$ $$z=(T-2)(36T^2+120T+37)$$ Or this. $$x=3(12T^2+16T-73)$$ $$y=4(3T+4)$$ $$z=2(3T+4)(12T^2+16T-73)$$ | |
| Aug 20, 2015 at 20:29 | comment | added | joaopa | @Individ: Maple does not agree with your solution. I took $p=4$ and $s=3$. With your first solution one has $$((T+1)X+TY-1-Z)((T+1)X+TY-1+Z)-24XY=10368T^3+13824T^2-58464T-41904$$ | |
| Aug 20, 2015 at 19:52 | history | edited | individ | CC BY-SA 3.0 |
added 169 characters in body
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| Aug 20, 2015 at 18:39 | comment | added | Turbo | Did anyone test this answer? by plugging in numbers? | |
| Aug 20, 2015 at 15:55 | comment | added | Igor Rivin | If it is easy to solve, it should be easy to explain how you got the solution... | |
| Aug 20, 2015 at 15:50 | comment | added | individ | @IgorRivin don't understand the question. The equation is easy to solve it. | |
| Aug 20, 2015 at 15:43 | comment | added | Igor Rivin | Would you care to elaborate on how you get these? | |
| Aug 20, 2015 at 15:15 | history | answered | individ | CC BY-SA 3.0 |