Timeline for How balanced can abc triples be?
Current License: CC BY-SA 4.0
13 events
| when toggle format | what | by | license | comment | |
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| Apr 5, 2020 at 15:19 | comment | added | Wolfgang | Oops yes that was too quick. I'll think again and check with the numerical triples... | |
| Apr 5, 2020 at 15:03 | comment | added | joro | @Wolfgang Don't you need epsilon in the denominator of the inequality? | |
| Apr 5, 2020 at 12:26 | comment | added | Wolfgang | Well, if the balance is $a/b=\varepsilon$, then in this construction, $A/B=\frac{(1-\varepsilon)^2}{4}<\frac14$ so indeed, that looks like my conjecture should be false for $\varepsilon <\frac14$. I would consider balances $>\frac14$ much more interesting anyway. | |
| Apr 2, 2020 at 17:56 | comment | added | joro | @Wolfgang my answer works for quality > 1 | |
| Apr 2, 2020 at 17:41 | comment | added | Wolfgang | I mean it indeed in the sense of @Wojowu. The threshold of 1.4 for a "good" one being kind of arbitrary.... | |
| Apr 2, 2020 at 12:16 | history | edited | joro | CC BY-SA 4.0 |
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| Apr 2, 2020 at 12:07 | comment | added | joro | @Wojowu I confused you with the OP, sorry. | |
| Apr 2, 2020 at 11:08 | comment | added | Wojowu | What do you mean with my conjecture? (are you confusing me with the OP?) And what do you mean with symbolic $a,b$ and their degrees? | |
| Apr 2, 2020 at 10:39 | history | edited | joro | CC BY-SA 4.0 |
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| Apr 2, 2020 at 10:22 | comment | added | joro | @Wojowu I suspect your conjecture is false by my construction when you work with symbolic $a,b$ and check the degrees of the triples. | |
| Apr 2, 2020 at 10:19 | comment | added | joro | @Wojowu Could be. I have seen explicit distinction. | |
| Apr 2, 2020 at 10:01 | comment | added | Wojowu | According to my google search yesterday, "abc triple" is often taken to mean a triple satisfying $rad(abc)<c$. | |
| Apr 2, 2020 at 9:46 | history | answered | joro | CC BY-SA 4.0 |