Timeline for Solving $z^n=a+bi$ using only radicals of positive real numbers
Current License: CC BY-SA 4.0
14 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 19, 2021 at 15:46 | history | edited | R.P. | CC BY-SA 4.0 |
edited title
|
| Oct 8, 2015 at 4:48 | comment | added | individ | I can't understand! What is not clear is the primitive solution of the problem. It also Pythagorean triples. $$u^2+v^2=\sqrt{a^2+b^2}$$ The decision boils down to this primitive idea. $$a=2uv$$ $$b=u^2-v^2$$ | |
| Oct 7, 2015 at 22:34 | history | edited | Hugo Chapdelaine | CC BY-SA 3.0 |
added 23 characters in body
|
| Dec 19, 2014 at 17:16 | history | edited | Hugo Chapdelaine | CC BY-SA 3.0 |
added 47 characters in body
|
| Dec 18, 2014 at 19:04 | answer | added | Alexander Kuleshov | timeline score: 0 | |
| Sep 21, 2012 at 16:40 | answer | added | Hugo Chapdelaine | timeline score: 3 | |
| Sep 18, 2012 at 18:29 | history | edited | Hugo Chapdelaine | CC BY-SA 3.0 |
added 73 characters in body
|
| Sep 18, 2012 at 18:00 | comment | added | Hugo Chapdelaine | Of course one has to be careful by the meaning of a "reduced writting". For example $\sqrt[5]{1}$ would not be a reduced writting for me since the 4 complex 5-th roots of unity can be written in terms of $\sqrt[2]$. I'm not sure at this point that I would be able to define properly what I mean by a reduced writting... But definitely an expression like $\sqrt[n]{1}$ (for $n>1$) would not be reduced but its reduced writing would only involves a succession of $\sqrt[p]{}$ with $p$ prime dividing $\varphi(n)$. | |
| Sep 18, 2012 at 17:50 | comment | added | Hugo Chapdelaine | There is at least the following easy observation: if $f(z)\in\mathbf{R}[z]$ has all its roots real then a (reduced) writting of a root of $f(z)$ in terms of radicals should only involve $\sqrt[m]{}$ with integers $m$ such that $\varphi(m)=2^r$, since for $p>2$ prime the group of $p$-th roots of unity cannot be embedded in the splitting field of $f(z)$ which is included in $\mathbf{R}$ by hypothesis. | |
| Sep 18, 2012 at 17:24 | history | edited | Hugo Chapdelaine | CC BY-SA 3.0 |
deleted 1 characters in body
|
| Sep 18, 2012 at 16:49 | answer | added | Will Jagy | timeline score: 8 | |
| Sep 18, 2012 at 16:22 | history | edited | Hugo Chapdelaine | CC BY-SA 3.0 |
deleted 77 characters in body
|
| Sep 18, 2012 at 15:42 | history | edited | Hugo Chapdelaine | CC BY-SA 3.0 |
added 5 characters in body
|
| Sep 18, 2012 at 15:34 | history | asked | Hugo Chapdelaine | CC BY-SA 3.0 |