Let {c1, c2, ⋯, ct} where t=ϕ(r) be a reduced residue system r. Show that c1+c2+⋯+ct ≡0 (r) .

Question

Let {c1, c2, ⋯, ct} where t=ϕ(r) be a reduced residue system r. Show that c1+c2+⋯+ct ≡0   (r) .

Accepted Answer

Step 1:u000ALetu0027s understand what weu0027re working with. A reduced residue system modulo $r$ is a set o

Let $\left\{c_1, c_2, \cdots, c_t\right\}$ where $t=\phi(r)$ be a reduced residue system $\bmod r$. Show that $$ c_1+c_2+\cdots+c_t \equiv 0 \quad(\bmod r) . $$