Timeline for Find all positive integers $n$ such that $n+\tau{(n)}=2\varphi{(n)}$
Current License: CC BY-SA 3.0
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| Mar 21, 2018 at 3:12 | comment | added | GH from MO | There is a more elegant way to finish. In your first display, each $d$ is odd, hence in fact we get $\tau(m^2)\leq m$. Therefore, we have equality in this bound, so each odd $d<m$ divides $m^2$. For $m>1$, this implies that $m-2\mid m^2$, hence also $m-2\mid 4$. As $m$ is odd, $m-2=1$, whence $m=3$. | |
| Mar 20, 2018 at 17:48 | history | answered | Alexander Kalmynin | CC BY-SA 3.0 |