We assume that the conditions of questions 12 and 14 are satisfied and that $\lambda(0) \neq 0$.
15a. Show that $\lambda$ and $\mu$ are periodic on $\mathbf{Z}$, with periods dividing $\ell$.
15b. Show that the period of $\lambda$ is equal to $\ell$.
15c. Show that the period of $\mu$ is also equal to $\ell$.