Be careful of spelling mistakes, you wrote \end{tickzpicture}
. Also, you can specify \radio
as \def\radio{3}
. A tikzpicture is by default on 1 = 1cm, so no need to specify it.
Finally, the error comes out because of this: ...:(\radio+1));
If you want to enclose a calculation, then you need to use curly brackets, because otherwise Tikz is going to confuse them with the other ones.
Also, since your \x
reaches 10, you need also enclose it within curly brackets, like $n_{\x}$
, otherwise, you'll get only the first number properly displayed, like in this image:

Update
If you want to add arcs that link the nodes, there are two ways. The first one would be to add this code:
\foreach \x [remember=\x as \lastx (initially 1)] in {1,...,\n,1}{%
\draw (n\lastx) to [bend right=10] (n\x);
\draw (m\lastx) to [bend right=10] (m\x);
}
The curves will be very similar to a circle, but not 100%. And here the second method comes in handy. Basically you draw two circles in the background and then fill the nodes with a white color. Now you have a perfectly circular link to all nodes. I would suggest this method.
Output

Code
\documentclass[tikz, margin=10pt]{standalone}
\begin{document}
\def\n{10}
\def\radio{3}
\begin{tikzpicture}
\draw (0,0) circle (\radio);
\draw (0,0) circle (\radio+1);
\foreach \x in {1,...,\n}{
\coordinate (cn\x) at ({(1+2*\x)*180/\n-90}:\radio);
\node[fill=white] (n\x) at (cn\x) {$n_{\x}$};
\coordinate (cm\x) at ({(1+2*\x)*180/\n-45}:{\radio+1});
\node[fill=white] (m\x) at (cm\x) {$m_{\x}$};
}
\node at (0,5) {Using circles};
\begin{scope}[xshift=10cm]
\node at (0,5) {Using a $\backslash$foreach statement};
\foreach \x in {1,...,\n}{
\coordinate (cn\x) at ({(1+2*\x)*180/\n-90}:\radio);
\node[fill=white] (n\x) at (cn\x) {$n_{\x}$};
\coordinate (cm\x) at ({(1+2*\x)*180/\n-45}:{\radio+1});
\node[fill=white] (m\x) at (cm\x) {$m_{\x}$};
}
\foreach \x [remember=\x as \lastx (initially 1)] in {1,...,\n,1}{%
\draw (n\lastx) to [bend right=10] (n\x);
\draw (m\lastx) to [bend right=10] (m\x);
}
\end{scope}
\end{tikzpicture}
\end{document}