Question 2
Let $(x_n)_{n\ge0}$ and $(y_n)_{n\ge0}$ be defined by
$$x_0=365,\qquad x_{n+1}=x_n(x_n^{1986}+1)+1622,$$
$$y_0=16,\qquad y_{n+1}=y_n(y_n^3+1)-1952\quad(n\ge0).$$
Prove that $|x_n-y_k|\gt 0$ for every pair of natural-number indices $n,k$.
$$x_0=365,\qquad x_{n+1}=x_n(x_n^{1986}+1)+1622,$$
$$y_0=16,\qquad y_{n+1}=y_n(y_n^3+1)-1952\quad(n\ge0).$$
Prove that $|x_n-y_k|\gt 0$ for every pair of natural-number indices $n,k$.