Chapter 4.4, Problem 28E

Use the Chinese remainder theorem to show that an integer a, with $0\le a<m=m_{\text{1}}{m}_{\text{2}}\mathrm{...}{m}_n$ , where the positive integers $m_{\text{1}},m_{\text{2}},\mathrm{...},m_n$ are pairwise relatively prime, can be represented uniquely by the n-tuple ( $a\text{mod }{m}_{\text{1}},a\text{ mod}{m}_{\text{2}},\dots a\text{ mod }{m}_n$ ).