Timeline for Has $\sigma\left(\sigma_0(n)^4\right)=n$ infinitely many solutions?
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
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| Jun 6, 2018 at 7:23 | history | edited | didgogns | CC BY-SA 4.0 |
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| Jun 6, 2018 at 5:47 | history | edited | didgogns | CC BY-SA 4.0 |
added 1946 characters in body
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| Jun 5, 2018 at 0:08 | comment | added | didgogns | From the original equation, applying $\sigma_0$ to both side gives $\sigma_0(\sigma\left((\sigma_0(n))^4\right))=\sigma_0(n)$ so $\sigma_0(\sigma(m^4))=m$ is derived. From $\sigma_0(\sigma(m^4))=m$, $4$-power both sides and applying $\sigma$ gives $\sigma(\sigma_0(\sigma(m^4))^4)=\sigma(m^4)$ so original equation is derived. | |
| Jun 4, 2018 at 17:05 | comment | added | N8tron | Can you elaborate on why $n=\sigma(m^4)$ is equivalent to the statement $\sigma_0(\sigma(m^4))=m$ ? I would think you'd need $\sigma_0$ to be injective for that to be true :) | |
| Jun 4, 2018 at 16:25 | vote | accept | CommunityBot | ||
| Jun 4, 2018 at 16:24 | comment | added | user243301 | You have magic in your soccer boots! Many thanks I am going to study it, and the linked MSE and Wikipedia. On the other hand $4.4\cdot 0.214$ was close to $1$. If you want to add some observation/calculation in next future feel free to do it. | |
| Jun 4, 2018 at 16:11 | history | answered | didgogns | CC BY-SA 4.0 |