Timeline for Exponential Diophantine $\prod x_i^{e_{x_i}} + \prod y_i^{e_{y_i}} = \prod z_i^{e_{z_i}}$ ,$e_{x_i}>3,e_{y_i}>3,e_{z_i}>3$
Current License: CC BY-SA 3.0
13 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 21, 2011 at 9:10 | comment | added | joro | For 3-full the only solutions I found are: 271^3 + 2^3 * 3^5 * 73^3=919^3 and 3^4 * 29^3 * 89^3 + 7^3 * 11^3 * 167^3=2^7 * 5^4 * 353^3 | |
| Jun 17, 2011 at 14:45 | comment | added | joro | @Gerry I couldn't find solution in the first 300 terms. | |
| Jun 17, 2011 at 12:15 | comment | added | Gerry Myerson | The question is whether the sum of two coprime 4-full numbers can be 4-full. The first 4-full numbers are tabulated at oeis.org/A036967 | |
| Jun 17, 2011 at 11:15 | history | edited | joro | CC BY-SA 3.0 |
Deleted nonsense
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| Jun 17, 2011 at 10:10 | comment | added | joro | @J.C. Ottem Thank you! I think I begin understand the second equation. Strangely to me some conics gave abc triples with quality 1.2 - 1.3 so I wonder should I delete the second equation or rephrase it sanely for abc triples... | |
| Jun 17, 2011 at 9:02 | comment | added | J.C. Ottem | @joro: The resulting conic curve is still homogenous, so there are lots of coprime integer solutions. | |
| Jun 17, 2011 at 8:44 | comment | added | joro | Taylor thank you. Added "integer" solutions, coprime was in the OQ. | |
| Jun 17, 2011 at 8:43 | history | edited | joro | CC BY-SA 3.0 |
integer solutions
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| Jun 17, 2011 at 8:14 | comment | added | Taylor Dupuy | For any fixed y and t this is still a rational curve and has an infinite number of solutions. | |
| Jun 17, 2011 at 7:27 | comment | added | joro | Thank you Gjergji. Edited the question disallowing $\pm 1$ | |
| Jun 17, 2011 at 7:26 | history | edited | joro | CC BY-SA 3.0 |
Disallowed y,t $\pm 1$
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| Jun 17, 2011 at 7:12 | comment | added | Gjergji Zaimi | Of course, your last equation has infinitely many solutions, take $y=t=1$ and the rest a primitive pythagorean triple. | |
| Jun 17, 2011 at 6:53 | history | asked | joro | CC BY-SA 3.0 |