VMO 1987 Problem 2

The sequences $a_0$, $a_1$, $a_2$, ... and $b_0$, $b_1$, $b_2$, ... are defined as follows. $a_0$ = 365, $a_{n+1}$ = $a_n$($a_n^{1986}$ + 1) + 1622, $b_0$ = 16, $b_{n+1}$ = $b_n$($b_n^3$ + 1) - 1952. Show that there is no number in both sequences.