AUSTRIAN-POLISH 1993 Problem 4

The Fibonacci numbers are defined by $F_0 = 1, F_1 = 1, F_{n+2} = F_{n+1} + F_n$ . The positive integers $A, B$ are such that $A^{19}$ divides $B^{93}$ and $B^{19}$ divides $A^{93}$ . Show that if $h < k$ are consecutive Fibonacci numbers then $(AB)^h$ divides $(A^4 + B^8)^k$