Elementary Number Theory – Reduced Residue System Modulo m and Sum Equivalence

Question

Show that if $c_1, c_2,\ldots, c_{\phi(m)}$ is a reduced residue system modulo $m$, $m \neq 2$, and $m$ is a positive integer, then $c_1 +\cdots+ c_{\phi(m)} \equiv 0 \pmod{m}$

From the problem statement, I only know that $\gcd(c_i, m ) = 1$.
Is there any related theorem that I missed?

A hint would be greatly appreciated.

Thanks,
Chan

Answer 1

HINT: If $c_i$ is a reduced residue class, then so is $m-c_i$. (Why?) and $\phi(m)$ is even $\forall m >2$