$b_1$ is always $1$ and $b_{\phi(m)}$ is always equal to $m-1$.
Ah, okay. Perhaps it'd be useful to mention that.
In particular it means that whatever $m$ is, 1 and -1 will always be their own inverse, and they will from a pair that are additive inverses.
(Assuming $m>2$.)
In particular it means that whatever $m$ is, 1 and -1 will always be their own inverse, and they will from a pair that are additive inverses.
(Assuming $m>2$.)