Timeline for For what integer $n$ are there infinitely many $-a+nb+c = -d+ne+f$ where $a^6+b^6+c^6 = d^6+e^6+f^6$?
Current License: CC BY-SA 3.0
13 events
| when toggle format | what | by | license | comment | |
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| Nov 10, 2015 at 9:09 | answer | added | Allan MacLeod | timeline score: 1 | |
| Nov 9, 2015 at 13:19 | vote | accept | Tito Piezas III | ||
| Nov 9, 2015 at 9:23 | answer | added | Allan MacLeod | timeline score: 6 | |
| Nov 7, 2015 at 13:35 | history | edited | Tito Piezas III | CC BY-SA 3.0 |
Much revised.
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| Nov 6, 2015 at 10:49 | comment | added | individ | Probably need to reformulate the problem as the solution of the system of equations $(1)$. | |
| Nov 6, 2015 at 4:24 | comment | added | Tito Piezas III | @GerryMyerson: I've changed the title to better reflect my intent. :) | |
| Nov 6, 2015 at 4:23 | history | edited | Tito Piezas III | CC BY-SA 3.0 |
Better title.
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| Nov 6, 2015 at 1:56 | comment | added | Tito Piezas III | @GerryMyerson: Of course, but Bremner's and Delorme's paper deals with the constraint that, $$a^2 +ad−d^2 =−(b^2 −be−e^2 )\\b^2 +be−e^2 =−(c^2 −cf−f^2 )\\c^2 +cf−f^2 =−(a^2 −ad−d^2 )\tag1$$ while Choudhry's has, $$a+b+c=d+e+f\tag2$$ This post does not obey $(1)$, but instead focuses on the constraint, $$a+nb+c=d+ne+f\tag3$$ and for what integer $n$ are permissible. | |
| Nov 6, 2015 at 1:50 | history | edited | Tito Piezas III | CC BY-SA 3.0 |
More details.
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| Nov 5, 2015 at 22:43 | comment | added | Gerry Myerson | I trust you're familiar with Bremner, A geometric approach to equal sums of sixth powers, Proc. London Math. Soc. (3) 43 (1981), no. 3, 544–581, MR0635569 (83g:14018), and Delorme, On the Diophantine equation $x^6_1+x^6_2+x^6_3=y^6_1+y^6_2+y^6_3$, Math. Comp. 59 (1992), no. 200, 703–715, MR1134725 (93a:11023) and Choudhry, On equal sums of sixth powers, Indian J. Pure Appl. Math. 25 (1994), no. 8, 837–841, MR1293455 (95k:11036) etc., etc. | |
| Nov 5, 2015 at 16:45 | history | edited | Tito Piezas III | CC BY-SA 3.0 |
Clarified questions.
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| Nov 5, 2015 at 5:05 | comment | added | Tito Piezas III | Incidentally, the smallest solution to $a^6+b^6+c^6 = d^6+e^6+f^6$, namely, $$(-23)^6+ 10^6+ 15^6 = 3^6+ 19^6+ (-22)^6$$ belongs to another family that is also true as $$3a+b+c = d+e+3f$$ | |
| Nov 5, 2015 at 4:56 | history | asked | Tito Piezas III | CC BY-SA 3.0 |