Section18.3Exercises

  1. Let \(Z_{p(x)}(n)\) be the number of solutions of the polynomial congruence \(p(x)\equiv 0\text{ mod }(n)\). Use facts from earlier in the course to show that this function is multiplicative (for a fixed \(p(x)\)). Connect this to the question of whether \(-1\in Q_n\).
  2. Show that the function \(g(n)\) is multiplicative, where \(g(2n)=0\), \(g(n)=1\) if \(n\equiv 1\text{ mod }(4)\) and \(g(n)=-1\) if \(n\equiv 3\text{ mod }(4)\).