Timeline for Find the general solution to the Forsyth/Abel functional equation
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 14, 2018 at 4:18 | vote | accept | mark | ||
| Feb 13, 2018 at 21:38 | comment | added | mark | Yes, you are right.... | |
| Feb 13, 2018 at 21:21 | comment | added | მამუკა ჯიბლაძე | @mark no it is not. For example when $g(1)=2$, $g(2)=1/2$ and $g(n)=1$ for all other $n$ you get the permutation $1\mapsto2$, $2\mapsto1$ and $n\mapsto n$ for all other $n$ | |
| Feb 13, 2018 at 21:19 | comment | added | mark | It is if $ng(n)$ is a permutation of the integers | |
| Feb 13, 2018 at 21:18 | comment | added | მამუკა ჯიბლაძე | @mark your $g(n)$ is not obliged to be integer | |
| Feb 13, 2018 at 19:09 | comment | added | mark | If one writes $f(n)=ng(n)$ (because $f(0)=0$) the equation becomes $mg(m)+ng(n)=R(m,n)g(R(m,n))$. If $f$ is a permutation of the integers then $ng(n)$ also is which suggests that $g$ is a unit, i.e., the $\theta$ in the proposed solution | |
| Feb 13, 2018 at 18:39 | history | answered | Robert Israel | CC BY-SA 3.0 |