Polynomial Diophantine equation under modulo

Question

This problem appered in my textbook and i cant solve it, it's in the chapter of the chinese reminder theorom so that's probably related. A solution or hint would be great.

Answer 1

$\require{AMScd}$Hint:By CRT we have a commutative diagram \begin{CD} \frac{\Bbb Z}{m_1m_2\Bbb Z}@>\sim>>\frac{\Bbb Z}{m_1\Bbb Z}\times\frac{\Bbb Z}{m_2\Bbb Z}\\ @VVV@VVV\\ \frac{\Bbb Z}{m_1m_2\Bbb Z}@>>\sim>\frac{\Bbb Z}{m_1\Bbb Z}\times\frac{\Bbb Z}{m_2\Bbb Z}\\ \end{CD} which maps: \begin{CD} x+m_1m_2\Bbb Z@>>>(x+m_1\Bbb Z,x+m_2\Bbb Z)\\ @VVV@VVV\\ f(x)+m_1m_2\Bbb Z@>>>(f(x)+m_1\Bbb Z,f(x)+m_2\Bbb Z)\\ \end{CD}