Timeline for abc-conjecture meets Catalan conjecture?
Current License: CC BY-SA 2.5
13 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 20, 2010 at 12:06 | vote | accept | Paul Hunter | ||
| Apr 18, 2010 at 21:45 | comment | added | Mike Bennett | Ahhh, I didn't notice the "edited" 2 days ago bit. Still, I guess the new version was what was intended... | |
| Apr 18, 2010 at 20:10 | comment | added | Kevin Buzzard | @Mike: what you're missing is that Paul Hunter has commited the cardinal sin of editing the question without indicating that he has done so (for example by writing EDIT in big letters just where he changed "|A|,|B|,|C|>M" to "|A|,|B|,|C|<M"), thus making my answer incorrect. If you click on "edited 2 days ago" you can see what the question used to be. | |
| Apr 18, 2010 at 19:56 | answer | added | Mike Bennett | timeline score: 2 | |
| Apr 18, 2010 at 18:52 | comment | added | Mike Bennett | I'm likely missing something here, but how, in Kevin's example, can one guarantee that the A, B and C are small? | |
| Apr 16, 2010 at 21:31 | answer | added | James Weigandt | timeline score: 1 | |
| Apr 16, 2010 at 17:58 | history | edited | Paul Hunter | CC BY-SA 2.5 |
Changed bounds in question to make it less trivial
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| Apr 16, 2010 at 17:51 | comment | added | Paul Hunter | Thanks and d'oh. My intention was that A,B,C were all about the same size as D,E,F,X,Y,Z (possibly smaller). I will have to rethink the question. (also X,Y,Z are meant to be positive) The relation to the ABC conjecture is possibly better illustrated with the (zero-testing) question: Given A,B,C,X,Y,Z, is A^X+B^Y=C^Z? (if Z is relatively large [compared with A,B,C], then C^Z > rad(A^X B^Y C^Z) = rad(ABC)) The relation to the Catalan conjecture is in the attempt to find "small" combinations of integer powers. | |
| Apr 16, 2010 at 9:23 | comment | added | Qfwfq | I don't understand your definition of "sparse integer". | |
| Apr 16, 2010 at 0:47 | comment | added | S. Carnahan♦ | ... so the answer is: Yes, because all integers greater than 1 satisfy this property. Could you could give some explanation of what this had to do with the ABC or Catalan conjectures? The connection is not obvious from here. | |
| Apr 15, 2010 at 19:42 | comment | added | Kevin Buzzard | ...alternatively, make X,Y,Z all very negative ;-) | |
| Apr 15, 2010 at 18:53 | comment | added | Kevin Buzzard | Umm...just choose D,X,E,Y,F,Z very large, with D and E and F pairwise coprime, and then gcd(D^X,E^Y,F^Z)=1 so by Euclid you can find A,B,C such that AD^X+BE^Y+CF^Z=1. Now if A,B,C happen to be too small just change them until they're not, e.g. A-->A+E^Y,B-->B-D^X. | |
| Apr 15, 2010 at 18:48 | history | asked | Paul Hunter | CC BY-SA 2.5 |