Timeline for Is the conjecture $min(A,B) \le rad(ABC)$ new and correct? [closed]
Current License: CC BY-SA 4.0
16 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 4, 2019 at 12:37 | comment | added | Đào Thanh Oai | @LSpice there is level of research I check by my computer 178 hours mathoverflow.net/questions/339813/… | |
| Aug 24, 2019 at 11:04 | comment | added | Đào Thanh Oai | I will research this conjecture with $\epsilon > 0$. | |
| Aug 24, 2019 at 5:47 | vote | accept | Đào Thanh Oai | ||
| Aug 24, 2019 at 5:47 | comment | added | Đào Thanh Oai | @YemonChoi Thank You, I Learn from experience | |
| Aug 24, 2019 at 5:31 | history | closed |
LSpice Yemon Choi Ivan Izmestiev abx Felipe Voloch |
Not suitable for this site | |
| Aug 24, 2019 at 3:26 | comment | added | Yemon Choi | I'm voting to close this question for the reasons indicated by @LSpice | |
| Aug 23, 2019 at 19:46 | comment | added | J. E. Pascoe | There are four counterexamples with $a \leq b < 10000.$ These were appended to my answer in a comment. The code I wrote is obviously unoptimized, (as it took about an hour to finish) so calculating all examples less than a billion would require actual thought. | |
| Aug 23, 2019 at 19:10 | comment | added | J. E. Pascoe | Not that I want to encourage naive conjecture here, but it seems to me that the conjecture seems to correspond to taking $\varepsilon = 0$ in the $abc$-conjecture, but correspondingly weakening the conclusion to be about the smallest number involved rather than the largest. So far, the Mathematica program I have been running has produced one other example with $a,b< 10000,$ which is $(1024,1377).$ Its possible there may be only finitely many counterexamples, but much like the $abc$-conjecture itself, I see no reason why. | |
| Aug 23, 2019 at 19:05 | review | Close votes | |||
| Aug 24, 2019 at 5:35 | |||||
| Aug 23, 2019 at 19:03 | comment | added | Robin Zhang | In line with the counterexample given by Pascoe, looking for differences and sums of large powers of small primes that only have a few distinct small prime factors probably gives many counterexamples. | |
| Aug 23, 2019 at 18:54 | comment | added | J. E. Pascoe | @LSpice, to be fair, it is true when $a, b \leq 1000.$ | |
| Aug 23, 2019 at 18:50 | comment | added | LSpice | Setting aside the fact that a counterexample was produced in an hour, surely MO is not the place to test conjectures that trivially imply FLT. It seems to me that, for such a conjecture, you need to provide some serious evidence that it might be correct before expecting other people to spend time on it. | |
| Aug 23, 2019 at 18:49 | history | edited | LSpice | CC BY-SA 4.0 |
TeX and proofreading
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| Aug 23, 2019 at 18:42 | answer | added | J. E. Pascoe | timeline score: 10 | |
| Aug 23, 2019 at 18:20 | comment | added | hookah | What you have in mind seems related to abc-conjecture, one of whose consequences is Fermat's last theorem. See here: en.wikipedia.org/wiki/Abc_conjecture | |
| Aug 23, 2019 at 17:40 | history | asked | Đào Thanh Oai | CC BY-SA 4.0 |