The discussion centers on proving that all points within a circle share the same center, using the metric $d_p(n+m)=|n-m|_p$. Participants clarify that the correct notation for the metric should be $d_p(m,n)=|n-m|_p$, which refers to the $p$-adic metric on the rational numbers. There is a request for a definition of a circle's center and clarification on the variable $p$. A link to a relevant resource is provided for further exploration of the topic. The conversation emphasizes the importance of precise definitions and notation in mathematical discussions.