Timeline for Diophantine equation Oeis A159589
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 30, 2023 at 22:13 | comment | added | John Omielan | @Twiga As for solving it, $449$ is prime so there are $2$ basic cases. With $\gcd(x,449)=d$, then if $d=1$, we can leave your equation alone, else $d=449$ so we can set $x=449a$ & $y=449b$ to get $b^2=a^2+(a+1)^2$. Then we're trying to find primitive Pythagorean triples, using the formula provided there, but also handling the possibility that $x$ and/or $x+449$ are negative. Solving the equations will then result in a generalized Pell's equation. | |
| Jul 30, 2023 at 22:04 | comment | added | John Omielan | @Twiga Welcome to MathOverflow. FYI, using an Approach0 search, the Math SE site's Can OEIS be used for searching of sequences of pairs? has an answer that states "... the solutions $(x,y)$ of $x^2+(x+31)^2=y^2$ are A118674, A157646". Thus, there is at least one other similar Diophantine equation in OEIS, but there's also no reason given for why it's there. | |
| Jul 30, 2023 at 20:59 | comment | added | Dima Pasechnik | oeis.org/A159589 gives a recurrence for $a(n)$ - so, yes, this looks like the full solution. | |
| Jul 30, 2023 at 20:46 | history | edited | Twiga | CC BY-SA 4.0 |
edited body
|
| S Jul 30, 2023 at 20:46 | review | First questions | |||
| Jul 30, 2023 at 21:45 | |||||
| S Jul 30, 2023 at 20:46 | history | asked | Twiga | CC BY-SA 4.0 |