Timeline for Can four integer numbers $x$, $y$, $x-y$, $x+y$ be powerful numbers where $\gcd(x,y)=1$?
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 4 at 14:26 | history | edited | LSpice | CC BY-SA 4.0 |
Link to comment
|
| Jul 4 at 12:02 | comment | added | Peter Taylor | Your solution checks out. | |
| Jul 4 at 10:54 | comment | added | joro | @PeterTaylor I edited with solution of size 146 digits. You have sharp eye for bugs, would you please confirm or disprove it? | |
| Jul 4 at 10:52 | history | edited | joro | CC BY-SA 4.0 |
Explicit solution of size 146 decimal digits
|
| Jul 3 at 16:42 | history | edited | Michael Hardy | CC BY-SA 4.0 |
added 27 characters in body
|
| Jul 3 at 13:11 | history | edited | joro | CC BY-SA 4.0 |
Added a near miss
|
| Jul 3 at 10:55 | comment | added | Peter Taylor | I don't have an intuition either way. Having infinitely many solutions is not sufficient because all of them might have the same obstacle with the stray 2, but it would be quite interesting if that were in fact the case. | |
| Jul 3 at 10:51 | comment | added | joro | @PeterTaylor Indeed, you are right, this is a near miss of the oddest prime 2. Do you think my approach may work? | |
| Jul 3 at 10:06 | comment | added | Peter Taylor | In the same question, Elkies gives a solution to $X^4 - Y^4$ is powerful, but it's not a solution to this problem solely because $\nu_2(X^2 + Y^2) = 1$. | |
| Jul 3 at 9:58 | history | answered | joro | CC BY-SA 4.0 |