1.6.55 Fields, Groups, Rings

condition: Let \( G \) be a cyclic group \( C_{n} \). Let \( a, b \in G \quad \) and \( \quad s \in \mathbb{N}, s \geq 1 \) such that \( a^{s}=b^{s} \), node \( (s, n)=1 \). Show that \( a=b \).