Timeline for Natural number solutions for equations of the form $\frac{a^2}{a^2-1} \cdot \frac{b^2}{b^2-1} = \frac{c^2}{c^2-1}$
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 9, 2020 at 14:58 | review | Suggested edits | |||
| Jun 9, 2020 at 16:29 | |||||
| Jun 9, 2020 at 3:17 | comment | added | Gerry Myerson | There are infinitely many integer solutions with $3b=4c$. Let $n$ be odd, and $(8+3\sqrt7)^n=x+y\sqrt7$, $x,y$ integers. Then $a=3y$, $b=x$, $c=3x/4$ is a solution in integers with $3b=4x$. $n=1$ gives $(9,8,6)$; $n=3$ gives $(2295,2024,1518)$. | |
| Jun 8, 2020 at 23:36 | comment | added | Gerry Myerson | For which values of $p$ does this lead to a solution in integers? Very few, I think. Your formula gives $b=8-28(7p-2)/(36p^2-7)$, and a linear over a quadratic can only be an integer for finitely many integers $p$. | |
| Jun 8, 2020 at 21:50 | review | Late answers | |||
| Jun 9, 2020 at 0:56 | |||||
| Jun 8, 2020 at 21:43 | history | edited | Sam | CC BY-SA 4.0 |
Typo for the (a,b,c) values. Multiplication factor "w" is missing & now shown by Sam
|
| Jun 8, 2020 at 21:43 | review | First posts | |||
| Jun 8, 2020 at 21:53 | |||||
| Jun 8, 2020 at 21:34 | history | answered | Sam | CC BY-SA 4.0 |