Timeline for A sequence based on Catalan–Mihăilescu problem
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 11, 2013 at 14:56 | answer | added | user9072 | timeline score: 7 | |
| May 11, 2013 at 14:54 | answer | added | Mike Bennett | timeline score: 5 | |
| May 11, 2013 at 4:57 | comment | added | Gerhard Paseman | Wlod: yes, for the problem as written, your form is appropriate. If one is looking for common differences between powers, 3^a - 2^c = 2^d - 3^b leads to a nice mod 8 restriction. I haven't taken it farther. Gerhard "Fast And Correct: Choose One" Paseman, 2013.05.10 | |
| May 11, 2013 at 3:26 | comment | added | Włodzimierz Holsztyński | @Piotr: for starters, you may check on pretty old papers where they got results about integers $n\cdot(n+1)$, and $n\cdot(n+2)$, etc. (not too much of that "etc.") which decompose into the product of a few first primes only. These problems are different but at least they can be viewed as relatives. | |
| May 11, 2013 at 3:20 | comment | added | Włodzimierz Holsztyński | @Gerhard "lightning fast" Paseman: Oooops, I was too slow, or the opposite, too fast. | |
| May 11, 2013 at 3:17 | comment | added | Włodzimierz Holsztyński | @Piotr: about the trivial solutions, isn't it simpler to forget them by assuming that both exponents $a\ b$ are greater than $1$? (Otherwise there are more trivial "solutions"). | |
| May 11, 2013 at 3:13 | comment | added | Włodzimierz Holsztyński | @Gerhard "positive tropism" Paseman: do you mean $3^a-3^b=2^c-2^d$ ? | |
| May 11, 2013 at 3:10 | comment | added | Gerhard Paseman | Oops. Sign Error. Even so, trying the appropriate formulation with powers of 3 on one side and powers of 2 on the other side might appear in the literature. Gerhard "Let's Take Absolute Values Instead" Paseman, 2013.05.10 | |
| May 11, 2013 at 3:02 | comment | added | Gerhard Paseman | You might find it revealing to study the system 3^a + 3^b = 2^c + 2^d. That will show some constraints on the possiblities and likely answer some of your questions above. Gerhard "Ask Me About Elementary Analysis" Paseman, 2013.05.10 | |
| May 11, 2013 at 2:41 | history | asked | Piotr Shatalin | CC BY-SA 3.0 |